The Cobra is a piece of crap: it doesn’t process Blood Bath, it’s slow to reload, and it’s slow to fire. Plus it’s a pain in the ass to get and it’s PINK! With bunnies! No thanks.
@biofobico: I’d go with this spec and grab a Love Thumper as soon as possible. The damage doesn’t really matter in TVHM, but the extra roid damage and explosive novas will help while rampaging. Speaking of which, don’t rampage until you see the red exclamation mark show, because Release the Beast doesn’t activate until then.
For the COM, I’d look for a good Rage Meat, with at least +5 Empty the Rage. The extra health and health regen will help while rampaging, just make sure you time your RtB activation properly. Look for a health relic and a singularity or tesla (bonus if it’s a Shock Storm) grenade for BL stacks. For weapons, anything by Torgue is great: I’d do Torgue’s DLC to start gathering tokens and gear. Gear doesn’t really get to be important until UVHM. By that time you should know what works for you and what doesn’t.
When you hit UVHM, you should do Hammerlock’s DLC for the Rough Rider* and get a new one every few levels for the extra health. If you do get a good RR, spec into Silence the Voices and get a sickle COM, preferably a Scream Sickle until you can get a Legendary version after level 62.
For leveling, I would max out Blood Filled Guns, Taste of Blood, Buzz Ax Bombardier, Fuel the Blood, Blood Bath, Boiling Blood, Nervous Blood, and Bloodsplosion in that order, but you can throw in StV after you’ve maxed out ToB for the extra damage resistance and then max out the others. By the time you’re level 50, you should have something like this. And by 69, it’ll look like this. You can put the remaining three points wherever you want. Note: if you’re going down the Hellborn tree, you should go all in because dabbling in it doesn’t do K much good - the same holds true for the other two trees.
*You can use a Love Thumper in UVHM with StV, but you don’t want to be using it in the Overpowered Levels. Note the roid damage will be transfered to you if you hit yourself in the head, so be careful. A health relic helps mitigate it because K gets all of his health back when he makes a kill while rampaging.
I also wouldn’t worry about the DLCs until UVHM unless you want to play them for the story. Since the rewards you get are locked into the level at which you first accept the quest, they may or may not be useful for long. At least in UVHM you can reset your progress and get one at a higher level. Plus gear only levels to 50 in THVM while it’ll always stay your level or near it in UVHM.
Forgot to add: an adaptive shield is a good choice until you can get a good Love Thumper or Rough Rider because of the extra health and elemental resistance. A Neogenator is a better choice, but stay away from any type of Turtle shield, especially the Hoplite. K has no shield recharge shields so he shouldn’t rely on shields to keep him alive.