Surviving in borderlands isn't as much about builds as it is about tactics, leveling up and gearing up.
For tactics: When you're overwhelmed, it's tempting to take out the bad guys smallest to largest. If you do that, you'll reduce incoming damage the fastest - BUT, you'll deprive yourself of "Fight for your life" opportunites. If you kill an enemy during "Fight for your life", you'll pop up with full shields! This is the main in-combat healing option.
For leveling up: do the side quests (lowest to highest). That bonus xp will push your level higher.
For gearing up: go to the last area you were able to complete. Bonus enemies will appear with extra loot. This is the best way to get a purple or orange weapon. For
example, if you're level 10, go back and clear Frostburn canyon (level 8).
Test all the weapons of blue quality and up, regardless of stats. You never know what kind of wacky gun gimmick might help.
In general, your build in early game does not matter much. Just make sure you phaselock those mutants as often as you can. If you are still uncomfortable with your build, try shifting into Harmony to heal better.
As for money, no, you can't store it in the bank, but just stop caring! Every time you die, you lose 7% of your current money—the less you have, the less you should be afraid of dying. I've never had problems with money—even if you miss that rare gun in the shop, it is not like you won't find a better one soon.
There even is a reason and a way to keep you money low voluntarily: Slot machines. There's a low but reasonable chance to win Eridium there, and as cost of playing rises with the level of main quest, there's zero point in saving for later—money inflates, Eridium doesn't! My personal way of playing is to burn all my money in slots after each trip to battlefield. Longest forays usually net me mostly two to three "rounds"—that is, gambling sessions that end in full inventory (of course, buy inventory upgrades first).
Gamble!
- No money - no fear of death!
- Accidental good gun!
- Average of 0.1916 bars of Eridium per pull!
- Eventual "Jackpot!" badass challenge!
The only thing you need a lot of money for is "For the Hoard!" achievement - and accumulating 3,000,000 is fairly easy even at the end of Normal, and trivial at the end of TVHM.
Best Answer
I'd basically recommend 2 shields.
first would be the bee if you wanna go pure dps since her skills restore shields on kills and it wouldnt have much downtime as a result. so you get quite the damage buff. However this comes at the cost of shields that would give you more survivability.
The alternative would be the sham. Absorbing bullets will give you more survivability (can go up to 94% absorb rate). Especially useful if using norfleet rocket (try to get a logans gun which is dropped from willhelm if you want to use rockets. while equipped with the sham, you can just shoot the ground with logans gun and absorb socket ammo from the splash explosions)