Start with a stripped lower (any reputable manufacturer will work). I've used Stag, DPMS, RRA and Essential Arms with out any issues.
I like to buy all the pins, springs, grip, trigger and "lower stuff" individually for my ARs. That way I don't end-up with a bunch of left-over parts from a factory "lower parts kit" that I'll never use.
Get a decent single-stage, non-adjustable trigger (I like the 3# Jard, but YMMV) and use some sort of locking hammer/trigger pins (KNS or the like). You don't want set screws coming loose on you in the middle of a match, and you surely don't want to lose a trigger/hammer pin.
Work over your BCG! Bad gas seals and weak extractors can ruin a good day. I'm talking flatten the gas key, locktite it on and stake the screws. Throw some extra power springs and a heavy-duty o-ring in there while you're at it. If you don't know how or don't want to do it yourself, send one out to be done or buy one already done... I think Denny sells some "super duty" BCGs over at Global Tactical already done.
Get a durable, comfortable, fixed, light weight stock. There is no need for telescoping stocks in 3 gun.
I like a 16" barrel with a medium profile and chrome-lined chamber and bore. 16" is more than adequate for 3 gun distances while keeping the weight low. I also think HBARs are over-kill here. My preference for the chrome-lining is just because I like to shoot Wolf (steel cased) ammo for high volume practice to save money. I feel better shooting steel cases in a chromed chamber.
On the subject of barrels... Get one that is threaded and put a good muzzle brake on it. You may think it's silly to put a brake on a soft recoiling .223, but fast follow-up shots are the name of the game. Every little bit helps (I even go so far as to add an Enidine hydraulic buffer to soften things even more).
For a forend, stay away from rails. There is really no need for rails on a 3 gun AR. They're just another thing that can get caught on clothes (or something else) and mess-up an otherwise good day. Smooth FFTs are the way to go.
I won't touch on sights much. Everyone has their preference. My eyes suck, so I use a Millett DMS-1 (1-4x) scope and shoot the "Tactical" division.
I do a couple other small things on some of my ARs that you may or may not want to do... I use oversized magazine release buttons, "tactical" bolt catches, tac-latches and Arredondo magazine wells.
A lot of AR building and parts selection is subjective, but if you start with a well-constructed base, you'll eventually end-up with a good, reliable AR for gaming.
