Don't be afraid to try new things. Even if you have a setup you really like, don't be afraid to branch out and try something new. New builds, new types of weapons, new tactics, just keep an open mind. Some things might surprise you with how fun they are.
Are you suggesting that moon should get off his ass and write some stories? He's like the Stephen King of gamefaqs. - Sorbz
First thing you should buy with your eridium is backpack sdu, second is the bank sdu, ammo isn't really an issue as you'll find tones in containers, and if you use a verity of weapons you'll almost never run out of ammo. Most of the challenges you can complete with out really making a conscious effort to complete them, so long as you use a verity of weapons/shields you'll eventually complete all challenges. The only exceptions would be for the kill x amount of enemies with an assault rifle while crouched, and kill x amount of enemies shortly after entering into iron sights with a pistol, so keep those in mind while using pistols and assault rifles. Never sell a legendary(orange rarity) item under any circumstance even if they've outlived their usefulness stash them in your bank, you'll be able to make use of them with another character. And one last tip, never ever ever ever accept death, after your chance to get a second wind runs out and the screen goes blue immediately pause and quit the game, it'll save you a f*** load of money. Also don't give killbot a fibber (just kidding snake)
"Okay, I'm sorry, Candy. I guess were not in America. I guess now, I'm not allowed to pay for sex with pennies."
Don't worry about saving your money, you can make money really quickly just by grabbing a pile of loot and selling it all. As such, feel free to top up ammo from the machines, or to buy gear from the machines if you happen to see something you want.
Some of the money related challenges can seem daunting at first (e.g. have 3 million cash on hand), but as things scale you end up making hundreds of thousands just from selling the loot from a run through an area, so again, theres no need to deny yourself little upgrades because you're "saving up".