I mistakenly went to Tiny Tina's docks when I thought I was going to the crater (Stupid waypoint is all shiny and distracting). So I unlocked that, hopefully not too early. It starts off hilarious enough, kinda want to go right into it now.
Torgue reminds me of 1 part Brawndo guy, and another part Michael Bay.
Definitely save Tiny Tina's for last. Well, definitely do Torgue + main campaign first. I'm not sure if there are any pirate references, but you've already done that one anyway.
From most people I've heard from, Hammerlock is the least engrossing DLC. I've only just barely started it, mainly to get The Rough Rider shield.