I'm the type of person that feels compelled to play things in order... so... yeah.
As for Axton, I built mine to focus primarily on his turret action skill. This is the build I was using:
http://www.bl2skills.com/commando.html#50550154015005014000055000155131
As I leveled I went down the Guerilla tree first, then the Gunpowder tree, and then the Survival tree.
The general idea was to give the turret the most firepower possible (extra shots per burst, increased accuracy, rocket pod, double guns, slag rounds, and ability to have two turrets down at once) and greatest utility possible (teleport to target rather than thrown, increased turret health, ability to stick to walls/ceilings so melee mobs can't hit it, shield).
As for gear, I focused on Sniper Rifles. Launch the turret, let it slag a bunch of enemies and draw their attention, then pick them off from a distance with Sniper Rifle critical hits. With talents giving passive damage to guns, damage to guns while the turret is out, and bonus damage against any targets that the turret has slagged... I never really had any problems killing anything. I generally stuck to high normal damage sniper rifles from Jakobs, but I also carried around a Fire and Corrosive sniper rifle as well, and the highest damage rocket launcher I could find for "oh shit" moments. For grenades I like Longbow Slag Bouncing Betties, but that's just my preference. For class mod I liked Engineer, since it further buffed my turret's damage potential beyond what I'm allowed in the skill tree and further reduces the cooldown. For the Relic slot I usually used a Sniper Rifle damage buff. For shield I typically used whichever one had the highest amount of shields to get the most out of my shield buffing talents (and since ideally I'm far from any real danger, so the vast majority of the damage I take will be against my shields rather than my health).
Hope that helps!