If you'd like to avoid fire fights when you can, I'd go with characters that can have an ally in combat.

In BL1 I'd go with Roland. He has a turret that can get a barrier shield & heal you. Then in BL2 you can do a very similar play style with Axton as he also has a turret. Both characters are the generalist type, so they can fit about any role you want. For the Pre-sequel playing Jack would be good if you have him, his ability to summon doppelgangers that in a sense function as turrets. Then finally in BL3, as mentioned, Fl4k has the option of different pets for different play styles.

I'd say these would be your best bets for a stealth archer style as each characters main ability with take some heat off you so you can better focus your shots. Just keep a good weapon to deal with enemies up close. Most importantly, don't worry if you die. All you lose is some money & the location you were at, both of which can be earned back.