I'll be picking Axton for my multiplayer playthrough, and Zer0 for my single player campaign.
I hate having the same classes in the same online game, and since my friend won't change his mind on Zer0... I have to pick Axton. I liked some of the skills he had (some skills are already released on IGN), like customizing the turret. My first pick was Zer0 because he looks badass, but when I looked more into his skills I found out that he had an entire skill tree based on sniping. I like sniping in Borderlands, and since I won't be having much lag in single player it's for the better.