how much accuracy do you want? I have a non free floated 16" mid leanth heavy barrel without crome that will shoot 3/4 - 1 MOA all day long. It will hold 2MOA with wolf ammo. So I would say get a good trigger, good (better yet great) sighting system, use quality ammo and you can have a 1MOA rifle all day long.
NOw that was accuracy, however if you are looking for bench rest accuracy for a Match than that is a whole new ball game. First get rid of any 5.56 chamber and get a 223 wyle chambering. free float that barrel, and make sure the barrel is a match grade from a great maker. I have Larue 18" 1/8 twist that shoots great, but is also cost more than the 16" mid. Speaking of twist that is next you need to know the range you want to shoot at, say you are only shooting 200 , you have more choices than if you want to do 1000 meter things. the faster the twist IE 1/7", 1/8" will shoot better with the heavy 75grain, 77 grain MK262 BTHP. now they will still do fine with the junk 55gre wolf shooting at milk jugs, but I don't know to many people that put that time and money into a rifle to plink with (Though I do know few).
After all that make sure the stock fits you. The leanth of pull needs to be correct so you and the rifle will fit togeathe. Next get the trigger that you like the best, not don't just go for expensive because some match trigger take some time to get used to and you might not like them. As a note you should remembe that the crome lining on AR15 barrels is for durability not accuracy. A stainless or non cromed barrel will out shoot a cromed barrel if all other things are equal. Most companies that sell stock Ar15's sell them with cromed barrels because for plinking, police partol use, and self defense they want the barrels to last longer, not be perfectly accurate.
Hope I helped.