Hm. Oh dear. Rapture is, to be quite honest, the closest thing the Jem series ever had to pure evil. This is a girl with very little in the way of either conscience or morals. Her main motivation in life appears to be her own amusement and the pursuit of money - one of her favourite tricks is to try and con some poor gullible soul into paying her a fortune for some worthless hunk of junk (see Stingers Hit Town) or pulling an exotic charade to cheat people out of their hard earned cash (See Midsummer Night Madness and That Ol' Houdini Magic). Whatever her faults, though, Rapture is clever. Perhaps in many ways the cleverest of all the Jem characters. She has a good understanding of both people and their emotions and weaknesses, suggesting her to be both perceptive and intuitive, but she uses those gifts for all the wrong reasons. She takes full advantage of Pizzazz's crush on Riot by convincing her to drink a 'love potion' which makes her sick - this is a good example of Rapture's lack of conscience, since when Pizzazz is taken ill, all the Stinger does is laugh. The prank is so bad that even the other Misfits are shocked by it!
Another good example of Rapture using her abilities to all the wrong ends is her treatment of the old woman's fear of death in that Ol' Houdini Magic. She uses that fear to convince the woman to give over large sums of money to the Stingers, and would succeed if not for Jem and Astral's interference.
It is unclear precisely what Rapture's origins are based on the series itself. Whilst I have heard that she was meant to join the Stingers in America, Riot's Hope suggests they meet in Europe, though under what circumstances is not given. The flashback clips from the Hard Hard Life video indicate perhaps that Rapture was not so much of a musician in terms of instrumental capability before she joined the group (though she is also perhaps the best singer in the series), since she often can be seen playing a tambourine and not the guitar that she's better known for in later times. It also seems to me that the Stingers adopted her somehow, since Riot is taking protective care of her in the same music video, offering her his coat when she's cold. My own feeling is that Rapture is of American birth and was perhaps studying in Europe when she met Minx and Riot, but that is pure speculation on my part.
Rapture has a strong interest in the paranormal and the occult, and these usually make up a large part of her schemes to con people. She is seen in the series performing magic, claiming (falsely) to host the spirit of Houdini, claiming to predict the future, reading palms and many other things. Her deceit regarding her tricks and games seems to me on occasion to be compulsive rather than a simple whim - almost as if she's setting herself the challenge of getting one up on whoever the target happens to be at the time. You can imagine that this kinda impish habit would get her into no end of trouble if it weren't for Riot's dominating influence in the band keeping her (more or less) in line.
There is one positive note to be said for Rapture's character, and that is that where her group is concerned she has absolute loyalty - more about that below.
Rapture is not really a 'friend' type of person. However, within the Stingers there is no doubt that she has absolute loyalty for them - a fact perhaps based on her trusting them and not people outside. I wonder if perhaps she owes them some big favour for taking them in, because her devotion to Stinger business is generally absolute. In The Day The Music Died, when Riot is missing, it is clear she is unsettled with the change. It also become apparent that the bond between her and Minx is one that sisters might share, since Rapture teases Minx about her failures with Rio, and goes to her in Midsummer Night's Madness when she's being chased by the crowd. Equally, when Rapture is drowning in That Ol' Houdini Magic, Minx is frantic to get her out, a favour returned by Rapture's clear panic when Minx is swept away by the tide in Change of Heart. However, the loyalty between the two girls wears thin when it's clear Minx needs support later in Change of Heart, suggesting both that Rapture dislikes change to the security of her world, and also cannot understand the deeper emotions that her bandmate is going through, probably because she has taught herself not to take any notice of them (Unfortunately I can find no indication in the series as to why she acts this way - the Stingers are not in enough episodes to find out enough about Rapture's roots, and it would be wrong of me to speculate so broadly on her)
Rapture has no love or respect for the Misfits. She treats Pizzazz like a puppet and disregards the existance of the rest wherever possible. She also has little love for the Holograms, Jem or Rio (she calls the Holograms 'mundane' in Straight From The Heart) Really, I don't think she likes anyone outside her own band! She develops the starts of a rivalry with Astral in That Ol' Houdini Magic, which you can only imagine continuing had the series gone on, and she's perfectly happy being utterly unpleasant to the drippy Regine when the designer has outlived her usefulness (perhaps the start of another, more general rivalry?)