After completing my very first playthrough on Easy (currently playing on Normal now), here's a few hints and tips that I thought i'd share:
1) After the beginning cutscene when Dan Hagar rescues you from the 2 Ghost Bandits, you can loot their bodies for an early cash grab!!!
(NOTE: The cash you get from those 2 guys is random)
2) Get the Monocular before going to the Ghost Hideout!! This little item tends to be skipped over by other players, but I find the scope it gives you for your pistol (double-barrel shotgun for the "Anarchy Edition" too) extremely helpful, as it provides instant headshots to your enemies if you're low on Sniper Rifle ammo
3) Craft plenty of items and ammo!!! Depending on which area you visit or re-visit, stock up on plenty of items to craft. Because when playing areas like the Shrouded Bunker for example, you'd want to upgrade the Fatboy bullets to the Fat Mammas for your pistol, because they'll down the Shrouded Minigunners with a few shots to the head when zooming in with your Monocular (especially when playing on the Hard and Nightmare Difficulty levels)
4) Don't be afraid to fallback to a previous area!!! If you find yourself about to be killed, let alone ambushed, fallback to a previous area and ambush any bandits/mutants that charge after you.
5) Do the Sewer missions before heading off to the Dead City for the first time!!! I say this, is because at the very end of the Kvasir's Sewer mission, there's a Rocket Launcher laying next to the top step that's easy to miss. Because picking this up early, the Outfitters shop will immediately start selling ammo for it and will make the Giant Mutant boss fight incredibly easy.
6) Re-visit Crazy Joe's Swamp and the Ghost Hideout for extra Night Blossoms and Comet Blooms!!! Every so often these 2 plants, particularly the Night Blossom, will re-spawn and allow you to collect them either to sell or to keep for medicinal recipes. However, there is a glitch you can exploit to make the Comet Bloom to constantly re-spawn by the Ghost Hideout, simply by entering and immediately exiting.
7) Stock up on Pop Rockets!!! One of the ingredients you can collect (especially when going for the "Master Chef" achievement) is one that makes Pop Rockets for your Shotgun/Double-Barrel Shotgun. Because this'll make fights with the Krakens and Large Mutants (those big ones that carry mortars) very easy (at least until you get the Rocket Launcher), although switch back to Buckshot if you have any Sentry Bots helping you fight, because the splash damage from the Pop Rockets will kill them too.