Gaige is fun (I think they’re all fun, but Krieg hasn’t caught my interest). Have a look at their skill trees and see what you think. If you start with Gaige and she turns out not to be fun, there’s no harm in dropping her and trying something else.
I’ll put in a vote for Maya. For solo play, Phaselock can get you out of sticky situations the quickest and most reliably of all the characters. For example: a loot midget pops out of an ammo crate and healthgates you with a lucky shotgun blast. You’ve got just enough time to pull off one trick before he finishes the job (and that trick does not include a one-shot kill):
Axton: drop a turret between you and the midget and get to cover
Zer0: go into Decepti0n and run for it or take your chances with a kill
Gaige: toss Deathtrap and hope the midget takes the bait
Krieg: let him knock you into FFYL, and start hitting yourself in the head (that’s his action skill, right? Who plays that guy?) 
Maya: Phaselock the midget, immobilizing him, and stroll your way to safety or have a go at leisurely shooting him in the crit spot.
Maya can take care of herself for healing (since you won’t have a buddy around to pick you up) with Elated, Sweet Release, Life Tap, and Sustenance. If you’re interested in sniping as a side job, Maya is arguably second only to Zer0 for her potential as a sniper too.



