I have a Rock River upper with a heavy stainless barrel and it is sub MOA with the right ammo. If you do a little research you will find a lot of people who are getting very good accuracy from these uppers (and the varmint upper). I would pay some attention to twist rate. If you're planning on shooting 75gr and 77gr bullets, you're going to want a 1:7 or 1:8 twist rate. Lighter, varmint type bullets are going to do better with a slower twist rate.
To me, the best compromise is to buy a good upper and put together your own lower. The parts you're going to want to swap out are mostly on the lower (assuming your upper has a good barrel and is free floated). So you'll want to upgrade your trigger (LaRue or Geissele), probably upgrade your stock, maybe swap out your pistol grip, play around with spring and buffer, etc. And lowers are pretty easy to put together.
Or you can go out and spend a bunch of money on a GAP, LaRue, JP, etc. and get a rifle that you know will be a tack driver.
And finally, be sure to leave a good chunk of money for a decent optic. How much magnification you need will be governed by the type and distance of the shooting you're doing. But you will want something with decent glass and, most importantly, that tracks well.