As far as teams go, I'd probably end up joining one of the Umbrella teams because, as someone said above, you don't have to worry about becoming friends with anyone or trying to save everyone. I'm sorry but when the end of the world gets here I'm pretty sure it's going to be one of those: "look out for number one" things and I'll definitely be looking out for number one.
Now as for characters, my first choices would be Chris or Jill because they're the most seasoned and they have the most experience in these types of situations but, at the same time, we run into the problem expressed above; saving everyone and their grandmother in the process. (And this problem arises with many other characters as well.) Knowing this, I'd probably team up with Jake, HUNK or one of the Outbreak folks for a while and then dip out on them later. Not entirely sure the end of the world is the best time to be making alliances; I'd rather go it solo that way I only have to worry about myself.