I just bought the GOTY edition with all of the DLC. Should I install all of them, one or two or so, or should I play the game through and then install one every few weeks or so? Advice? I hear one of them has a bank which would be really nice to have. I would like some really killer guns too.

Install them, and just play them whenever you feel like it. I mean, you can go and play part of Zombie Island or something, and then leave. Also, you can't really play a couple of them until after beating the game, so don't worry about that. 
 
And don't play Moxxi. Just don't. 

Just install them all. Play through the main game, then go through the DLC in the order they were released is what I would recommend. I guess you can enter the Underdome anytime for the bank.

Far as I remember, the best order was finish the game first, then play Dr Ned's Zombies and then Knoxx.
Dunno about Claptrap (not even in the goty right?) and Moxxi's, Moxxi's for all levels I suppose but its nothing special.

The only odd thing is that you use the fast travel to get to the DLC which you don't actually get working till a little bit into the story. But I would certainly install all of it, as for when to play them I can't say, haven't gone through any of em.

Play through the main game first man. Not only do you need to reach a certain point first before you can fast travel, but you also need gather some of the really useful guns and equipment in the main story before you take on the DLC.