Borderlands

Don't pay too much attention to "specializations", every weapon can be good on any character.

Corrosive weapons are great, find a good x3 and x4 one and it'll probably last you most of the game.

Don't be afraid to mess around with character builds, you can always respec for money.

Most areas connected to the main world map has a Claptrap that, if repaired, will give you extra inventory slots.

Once you get to New Haven, you can essentially have as much money as you want by doing repeated treasure chest runs/quit/reload/repeat.

Transfusion grenades (the ones that drain enemy health) are extremely useful, require no aiming and can save your life. It will go to whichever teammate is closest, so you can heal them if they need it)

On Zombie Island (the only DLC I've played), make a beeline to the Southwestern area of Hollows End and talk to Zombie TK Baha and get the Brains quest, which will require you to get hundreds of brains from zombies.

The best order to do the DLC in, due to level scaling, is: Armoury Of General Nox, Claptrap's Robot Revolution, Zombie Island of Doctor Ned.

Don't really worry too much about running out of ammo, there's tons of lootable containers that have plenty of ammunition. Later on, you'll find class mods and guns that regenerate ammo.

Soldier has the easiest time playing solo, as the turret can be made to heal you and regenerate ammo. He's also a must for multiplayer for the same reasons.

All the character classes can use all the guns effectively. Although each class has skills that will enchance certain weapon types, there's nothing stopping you from giving your Hunter (the sniper class) a shotgun. It's also more beneficial to power up your action skill. My hunter's Bloodwing instagibs large mobs of enemies, barfs up a ton of loot when he hits then and heals me once the bird finishes it's little rampage, all because I invested all my points into his action skill abilities. If you're a competent FPS player, you won't need the minor skill boosts and buffs.

You don't have to do all the sidequests if you don't want to, but definitely do the Clap-Trap rescues, as they give you more inventory space. Also do the King-Tossing sidequest, the boss there drops a unique shield called Wee Wee's Super Booster. It'll have green text and no item description, but it's one of the best shields in the game, as while it has low capacity, it recharges quickly and more importantly, it regenerates health fast.

If you're not gonna get all of the DLC's, at least get Mad Moxxie's Underdome Riot and the Secret Armory of General Knoxx. Moxxie gives you access to a Stash feature like in Diablo 2 and similar loot RPGs, and Knoxx raises the level cap to 69, and has decent content.

If you kill an enemy with a melee attack you still get proficiency experience for whatever weapon you currently have in hand. You also get proficiency experience if a teammate, Bloodwing or Scorpio turret makes the fatal hit.