For a relationship, then definitely April Ryan. She's one of the most realistic and grounded characters I've ever seen in a game, she beats Zoe from Half Life 2 hands down. I really love Funcom for the way they handle character development. Plus, April is a sassy, smart person in her games, and has a great personality that I share to some degree. Plus, she's bloody attractive too:
It's worth noting that the third picture is my personal favourite; it's fan art from Deviant Art.
As for a best friend, I'm much less certain. Possibly Ezio, as he'd be pretty cool to hang around with, seems like a really fun guy, and he'd probably be the best wingman ever when we're out drinking and schmoozing with the local Italian ladies. It'd be awesome hanging out with Scott Pilgrim and his friends/allies, plus he'd be able to introduce me to Lisa Miller (assuming she's in the game in some way...) ;D. And I wouldn't mind going for a drink with the ODSTs of Halo 3: ODST, though to be fair that's partially because I'm also a massive Firefly fan...