all those games are great, however, I would scratch off Saints Row & Crackdown since they are kinda similar to GTA 4 and since you are just starting your 360 library, you may want something completely different.
I felt Lost Planet was a little weak. A good rental but not a keeper.
Burnout Paradise is a blast if you like arcade racing.
Gears of War is really good but the sequel is coming out in Nov. You might just want to rent the 1st one for the story (or lack of one, heh). and again Bioshock is amazing but once you beat it, that's kinda all there is.
Personally, I'd go with Oblivion which I have put 100s of hours in if you like open ended free roaming style of RPG games. You can be a Knight, a Wizard, Assassin, Thief, Warrior, all kinds of stuff.
However, I played this back in 06 so I don't know if it's considered dated or not.
EDIT: I just read this is for your sister? how old is she? what kind of games she likes? I'm confused. Her birthday so you're getting a game? for yourself or her? lol.