I'd recommend going with a game that she is interested in, and that you are good at GMing/explaining. Hopefully, there should be some overlap with these two elements. For example, I'd probably use either 4th ed. D&D for fantasy, Star Wars Saga Edition (R.I.P.

) for sci-fi, or the card-based Marvel SAGA for supers.
The classic Basic D&D Red Box worked well for me, and a similar method may work if you or she prefers to start with a 1-player game. However, many tabletop RPGs are about the group play dynamic, so starting her off in that context may be useful (and, it can divine/share the instruction among you & the group).
FWIW, I'd recommend against having her start off in an existing game with existing characters (if she's into gaming, and interested in participating, then it may be a cool way to go).
If you have the 4e CharBuilder, then creating a character is relatively quick and painless (that is if you go the 4e route). Any class should do fine, since the demands of play for each class is the same—it's just the role taken in the game.
In prior editions of D&D, I'd recommend a beginning player starting off with a fighter: it's simple, straightforward, and serves as a foundation of game mechanics knowledge. Other game elements (spells & whatnot) build on top of this, and the level of (relative) complexity goes up.
In any event, I'd recommend that starting off at 1st level/new character start point for non-level games (perhaps as a mini-game, or even a fresh start if that would work out) would be best. It'd provide a frame of reference of how a game starts, and how it progresses. After she gets the feel of the game, then she could create a power/level-appropriate character for the current game, or you could even simply boost up her first character to the equivalent level if she wants to use that PC in the ongoing game (that is if the new game doesn't become the new ongoing game, of course).