I would recomend that you read [i]The Competitive AR15[/i] by Glenn Zydiker. It will answer most of your questions about tightening up the AR. Spicific advice I cannot give you without knowing a entire scope of what you want to do with this rifle. If you do plan to shoot Service Rifle, you should obtain the rules from the CMP at [url]www.odcmp.com[/url].
My basic recomendations would be:
Service Rfle: Your choice of AR (I would go with Bushmaster, Colt, DPMS, or Armlight) with a 20" Wilson, Kreiger, or Oberhausen barrel (1 in 8 twist). The trigger could be left stock, that is largely a personal decision, go with what you are comortable with. Float the forend, nothing you do will have as much affect on your accuracy as a float tube will.
Match rifle: I do not know as much abouit match shooting, but the rules are much more lax than Service Rifle. I would look into a 24" barrel with your choice of sights. I would also float the barrel. That will get you started in the right direction.
You can shoot 1000yd with an AR. A friend of mine shot his DCM legal (20" barrel) at Perry last week and scored 187 out of 200 using 80gr shells. The rifle is capable of making long shots.