Roxy has the reputation of being the 'nasty' misfit...having watched her through several episodes I still fail to see why. I think people are too quick to judge Roxy at face value, and don't see all the things going on just beneath the surface. She's a high school dropout from a bad neighbourhood who has a desperate need to be someone, and who bluffs her way through life because she's ashamed of her lack of reading skill, among other things. Sure, she's rough and tough and quick to raise her fists, especially where Jetta is concerned, and judging by her hometown friends in Roxy Rumbles she's been in her fair share of scrapes, but she's not all violence and threats - she has her weaknesses. She has a fear of heights (Music Awards Part 2) and a sweet side to her nature which comes out at the end of Roxy Rumbles.
In Truly Outrageous, it becomes clear that there are issues with Roxy as a character. In terms of grabbing the spotlight, she really doesn't have much opportunity to make herself known as a character and this makes it hard to know how to take her from the off. It's only once the series proper begins that you get some real clues as to what makes this girl tick. It's perhaps more correct to call her the TOUGH misfit.

  Roxy is the kind of character who grew up taking care of herself - she has no concept of love because she has never been loved. No mention of parents is ever made for Roxy, but whoever they were, I have my doubts that it was intended to be even close to a happy childhood.
Roxy is fun to watch for one main reason - 95% of the time she is out of her depth. Having more or less brought herself up, her reactions to things are often childish and immature, but it's still clear that she's a kid who grew up far too fast.  I always wonder if she's meant to be a kid who was abused - she certainly has issues with people touching her. And, as I mentioned above, it's made very clear in Roxy Rumbles that Roxy dropped out of school. The age she did this is debatable.
There are other clues in the series though to Roxy and where she came from. Two stand out very prominently in my mind. In The Music Awards, Roxy treats the complaining of the Starlight girls as rather ridiculous. Her comments are, more or less, that they have food and a roof over their heads - why are they complaining? The other incidence is in Treasure Hunt when the urchins explain their philosophy of no favours unless you pay for em, cash in advance. Whilst Stormer stares on, bemused, Roxy is nodding her approval to every word. Clearly, then, this girl has had a dodgy past and has probably lived rough at some point in her life. No wonder she's grown up as tough and as physically adept as she has!

Well, there's no getting away from this. As Kimber so correctly surmised in her diary, Roxy can be ignorant. She can also be naive, but it's not the same kind of naivety that Stormer or Kimber herself sometimes exhibit. It's more a question of being out of touch with what's going on, of things passing over her head because she's always been her only role model and she didn't know what to teach. Two clear  Roxy personalities emerge from the episodes - the tough girl with the smart mind and the dumb girl who shows signs of vulnerability. I like both incarnations. She's one of those characters who seem to 'mellow' over time - the more you get to know her and things about her the easier she is to relate to and like. She's perhaps an easier character to handle too when she has to contend with Jetta 'horning in on their act', because the balance of power is less certain and she has someone to vy with for second in command within the Misfits. Despite her ignorance, however, it's maybe interesting to note that Roxy is the only character who never believes in Jetta's charade and always takes every opportunity to tease her about it
Though she has clear fears she doesn't usually let them get in her way - she has too much importance placed in her tough veneer to allow herself to appear weak to the people around her, though I get the feeling that maybe she could talk to Stormer if the need arose.
Finally, Roxy is impulsive. Reckless and impulsive, usually. It's a dire combination which is part of that Misfit charm, but doesn't do them any favours in terms of successful scheming! Basically, Roxy is the hands on girl. If it needs kicking, thumping or fiddling about with, Roxy's the one to ask....but delicate was never in her vocabulary!

Roxy On Music
Roxy is the only Misfit other than Stormer, who writes all the Misfit music anyway, to attempt to write a song of her own (I'm Gonna Change - she must've written it herself) and unlike Pizzazz, she can really play her instrument. Not only that, Roxy's musical prowess is clear in other areas. In Danse Time and Starbright Part Three she plays drums, and on one occasion I believe she has Stormer's synth...though that could just be animation :P.. 
I've always assumed that Roxy is the bass guitarist for the Misfits. This is largely based on the fact that the animation for the start of I Like Your Style and for Universal Appeal, the bass notes are played over the top of animation of Roxy and her guitar :) Not only that, but Roxy's own song has a strong and significant bassline running through it. Just seems logical to me. Despite this, however, I believe she's more than capable of playing lead guitar if the need arises. Though it's fairly easy to suppose that she's had no formal tuition in her instrument, she definitely knows what she's doing with it, and I think the series could have done more with her abilities.

Roxy On Life
Something that can't be omitted is Roxy's ability with figures. Even though she has no time for education and struggles to read, she isn't stupid. In Roxy Rumbles she's wise enough to know how much of her money she's losing from the tax people, and also even that Eric is shortchanging her on her wages at the start. And then, of course, it is ROXY who, in "The Day The Music Died", points out that the Starlight Girl's costs are coming out of the Misfit profit. Not only that, when Eric suggests a new Misfit in Talent Search, Roxy's comment is "Who needs a four way split?" yet another reference to her financial grasp of things, since she is clearly referring to the division of royalties and profit. This all suggests to me that the idea Eric is cheating Roxy out of money is unfounded. Of all of them, Roxy is the one who is perhaps most clued into (and interested in) finance. Since the only evidence of Eric wheeler dealing with her comes in Roxy Rumbles, moments before she walks OUT on the group, I think it's fair to say that Roxy knows precisely how much money she should be getting!!
Another thing about Roxy is her use of totally nonsensical phrases/threats at appropriate moments (Roxy-isms, perhaps). Remarks such as "I'll blow it out your ears!" or perhaps the more profound "Woah, this place smells like horses!" about a stable in Britrock can;t help but make you laugh :) It's not that she;s trying to be funny, she just is.
A character trait which I find fairly endearing too, is her love of food. Clearly again another indication of a hard past, Roxy always eats as if she doesn't know where the next meal is coming from, and it's not uncommon to find her snacking, or complaining about the lack of vegetables (!) on the train across America, sparking Jetta's assault with the mashed potato (Rock and Roll Express)
She hasn't a very long concentration span, perhaps because things frustrate her, since she's had none of the educational background that you have to assume the other three have had. She's far from stupid, but she's insecure about her own lack of knowledge in certain areas, so she reacts badly to being called dumb (as in her reaction to the contents of Kimber's diary in Scandal). If Roxy had been animated today, I have a strong feeling that she'd be a dyslexic character. Coming from a family myself with dyslexia in the genes (though I thankfully escaped it) she shows a lot of the signs to me of being dyslexic.
Finally, then, there is Roxy's love of gadgetry. You find a machine to fiddle with, wreck or just utilise and Roxy's usually about, tinkering at the controls to see what happens. In Broadway Magic she tampers with the stage controls - and realises she's hit the wrong dials, too. In Starbright #2 she sets off the explosions on the set early (ok, so thoughtfulness was never her strongest point). And you just gotta know it was Roxy who hotwired the Roadster in Intrigue at the Indy 500. It's also possible, if you want to bother justifying her strange desire to attract Jeff Wright in Starbright. Because this is so out of character it's generally put down as being written in before the later character roles were defined, and I support this view myself. However, Jeff is a stuntman and is au fait with gadgets, machinery and living it rough. To me that could be the ONLY justification for Roxy's interest - that Jeff is as wild of heart as she is. But I admit, it's a tenuous stretch of the imagination.

Roxy is closest in the band to Stormer, perhaps partly because Stormer is someone she easily 'outranks' in the pecking order. The more you watch the series, the more obvious it becomes that these two have a bond between them, despite how different they are. Stormer knows Roxy can't read, but it doesn't appear that Jetta or Pizzazz know this till after the TV show goes wrong in Roxy Rumbles (else surely Pizzazz would have prevented the chaos?) It's Stormer who helps Roxy through the hard walk to safety in Aztec Enchantment - at the point where they meet Jem's car train, Stormer is helping Roxy along. Roxy and Stormer sit together on the plane to China, and there are numerous shots of the two of them together, not to mention banter exchanged. Stormer even gets quite upset when Roxy walks out on the Misfits in Roxy Rumbles! You can't help feeling that in a way, Stormer looks up to Roxy as a strong role model, and Roxy looks to Stormer for the kind of sisterly support she never had.
This 'friendship' is more visible after Jetta joins the band. However, before it's sometimes easy to believe that Roxy has/wants equal power in the Misfits to Pizzazz (she comes up with several schemes, and wants to pick up their music award before Pizzazz shoves her out of the way).  In 'Adventure In China' she actually
assumes the role of lead Misfit, taking total initiative throughout the episode. She is also not afraid to stand up to or mock Pizzazz (In 'The Music Awards' she mocks Pizzazz' crash landing of the hanglider, and in the Jem Jam she shakes Pizzazz violently in anger when she finds out they're stuck in the dog kennel till the Monday morning) However, before Jetta's arrival in the band Pizzazz and Roxy are almost double trouble - there is a definite bond there which never completely breaks down, though Roxy later becomes more submissive to Pizzazz's leadership instead of asserting her own ideas.
She has no time for Jetta, stating that she'll be 'trouble' when the others want her to join the band (again possibly pecking-order related, however Jetta is a bright girl and perceptive as to how to wind poor Roxy up. A war of words is not something Roxy can ever win with Jetta, although you can't help feeling that if it came to fists, there would be a different outcome. Heck, even Pizzazz is afraid of Roxy in a temper! (See capture)
Jetta and Roxy are a definite personality clash. Roxy is jealous of Jetta's immediate bond with Pizzazz, whilst Jetta herself finds Roxy both irritating and an easy target
for her teasing. Their rivalry is put aside on the odd occasion, however, for example in 'The Jazz Singer' they team up to sabotage Ace O'Toole's boat and in 'Roxy Rumbles' Jetta is forced to admit that the band needs Roxy. They also team up in The Stingers Hit Town parts 1 & 2, when crisis in the form of Riot) hits the  band. However the squabbles between the two make for some funny moments!! (And usually end up in chaos!) Pizzazz often has to interrupt their disputes before they come to blows, and it is Jetta who first makes a joke about Roxy's illiteracy, sparking Roxy's departure from the Misfits.
Like Stormer and Jetta, Roxy is vastly insecure about her role and status within the band, but unlike Stormer, she never discovers that the rest of the band can't manage without her.  As a result there are times when she looks/acts downright miserable about things. My feeling is that Eric's teasing about replacing her in the band (Talent Search 1) had a deeper impact on Roxy than any of the other Misfits realise. When she's drawn back into the Misfits at the close of Roxy Rumbles, it is on a contractual technicality, and she only returns to the group
because she sees she has no choice. This suggests to me that Roxy needs a bit of a pep talk about her own ability - she certainly has plenty of it.
As for her relationship with the Holograms, she seems to have picked out two sparring partners among her foes. Right from the start she and Aja clash, after one of 
Roxy's more harebrained schemes goes awry, whilst she finds great pleasure in tormenting Shana in 'In Stitches' about her talent for design. I don't know which she dislikes's kinda hard to tell for sure :) She also has a brief go at Kimber when she tries to lure Jeff away in Starbright, but this seems so out of character for the Roxy that develops later on that I'm not sure much emphasis can be put on it (See also Roxy On Life)
One other set of friendships has to be brought up here also, and that is her friendship with her hometown friends in Philadelphia. She obviously both feels comfortable with them and is loyal to them - even after so much time she recognises them - and its clear she's hurt when Jem lures them away to 'learn to read'. It's important to note at this juncture that, aside possibly from Stormer, BaNee is the only character in the series who actually cares enough to want to help Roxy read, and BaNee's kindness inspires Roxy to try. I think Roxy could be a softie, if only she'd learnt how!