I have an inexperienced player joining an existing 7th level campaign.  Another factor is that she is often pulled away from the gaming table.  I want her to play something straight-forward with out a ton of options, that is why Fighter-Champion came to mind.  She is up for playing anything as long as it kicks butt!  The party doesn't have a rogue so in a perfect world that is what I would suggest she plays but since we aren't starting her at 1st level it might be too complex.

Any suggestions?

I’d say champion fighter is the simplest class. Once she gets a hang of the game, just switch her class. Or multi class her into warlock eventually.

Or just multi class into rogue...cuz then it’d be like starting at lvl 1 again with another class.

Rogue is not too complex. Champion fighter is probably the easiest class, but most rogues are also super straightforward, and they have a lot more utility out of combat as well. Obviously don’t force your player to play anything she’s not really into, but if she’s up for it and the party needs it, rogue is very appropriate for new players.

Purple Dragon Knight fighter might be easier.

edit: It’s also in need of improvements.

Yeah, champion fighter is easy. Same with berserker barbarian (but that sucks). Any character without a pool resource or spells should be easy enough.