i would appreciate those suggestions! just finished the main story on normal. not sure about playing to UVHM.
My recommendation for starting UVHM is as follows.
1) Try to start below lvl 50 if you can.
2) Get as much gear equivalent to your level as you can from farming the red chest at the end of Hero's Pass just before the entry to the Vault of the Warrior. This is an easy farm, as you can save and quit at the start of the vault of the warrio, then immediately transition back to Hero's Pass next to the chest, open it, take any decent loot, go back to the Vault, save and quit then rinse and repeat.
3) Get to Sanctuary by following the story quest only and ignoring all side quests. Get as much level gear appropriate stuff as you can from using golden keys at the chest in sanctuary.
4) Start farming the Marcus Mercenary final boss for loot and get yourself to level 52 in the process, at which point a wide range of legendaries will start to appear.
5) Once you have a few class appropriate legendaries proceed through the main storyline, returning to the Marcus Mercenary day to farm new legendaries every three levels or so.
6) I also advise watching a video guide on how to farm the Lyuada in The Dust early on, as this legendary weapon can be a huge help to any class.
7) After level 52, start the Tiny Tina DLC and get to the Forest zone, then start farming the ents in the forest for the Bee shield.
edit: i dipped a toe into the tiny tina stuff as per the rec above, and promptly started getting 1-shot by creatures. gear/lvl problems, i assume.
The skeleton mobs in the Tiny Tina DLC are really tough and I think the whole DLC is pretty tough at TVHM difficulty.