What are some good addons to customize my UI?
There are so many out there, it's impossible to suggest specifics - everyone has their own preferences. To me, the absolute minimum would be:
Omen
Recount
DBM (DeadlyBossMods)
Gatherer
Added to that, a unit frame mod (X-PERL is a good one to start with, and many people stick with it throughout) a combat text mod and a bag mod (Bagnon served me well for a while, and I still keep it installed for the Bagnon Forever tooltips, even though I don't use the rest of it any more). It may also be worth looking in to full UI mods like Tukui or LUA - these can be tweaked to customise them to your preference, but come as a fairly solid package in their own right. The best way to do it is just to experiment.
One of mine from our most recent Nef downing:
And middle of Cho'Gall from earlier that night, which better shows the combat text mod I use, Parrot:
Incoming healing/damage circles round the left, outgoing healing/damage round the right, buffs/debuffs/cooldowns scroll up from the top and important messages come up bigger and shake in the middle of their respective areas. In motion, it looks sick.
We're 2/13 down in HC content now, working on Atra next. One of our server recruits, Orjan (or Jeff), has posted up a Youtube video of our Chimaeron HC kill, but I can't link it here because Saith made it unsuitable for public viewing. You can check it out by searching for "Bans Hammer Chimaeron HC" on youtube (damn you, Jeff, and your sloppy grammar!)
Edit: edited for linky pics - click for higher res
