If your playing as the Siren, start with Diva and get Inner Glow (So you can heal while phasewalking.. helps a lot).
Get 3-4 points into Mind games eventually (15-20% is all you really need.. every other bullet will daze).
Get Phoenix ASAP (Saves ammo + Wrecks any enemy that burns). You'll be able to kill bandits just by touching them.
Look for a decent elemental SMG (Fire works great, Corrosive for Badass enemys and bosses that dont burn) until you can find a Hellfire. (Beat Playthrough 2 with a lvl 21 Hellfire Ez)
Keep a shotgun on switch for elemental enemies or bosses (Eventually I found a Corrosive shotgun which raped)
Controller ElementalDiva (5) Quicksilver & Spark (5)
Inner Glow (5)
Girl Power (5) Resilience or Intuition (Either resistance vs elements, or FrW and more Xp)
Mind Games (3-4) Phoenix (5 ASAP)
I used this build and it annihilated both play throughs. The only problem you'll have is some pesky enemys near the end that have a lot of shields.
You'll need a lightning SMG, or you can just respect and get the Assassin side for more normal Dmg.
Look for Firefly or Mercenary Mods. I stuck with Firefly (+Phoenix saves on ammo) until I found a Mercenary Mod with ammo regen (In playthrough 2 you might find one if your lucky)
http://zfire.free.fr/BL/ - A link to all the Red/White chests. Red give better guns, so l8er the white chests will just give crap guns for $$.)
If you dont have the DLC/any of the patches, you can farm New Haven chests which usually always gave me a Hellfire (Was like the most common rare SMG i've seen)