The less expensive button barreled rifles are very good shooters. I have no problem using them. Criterion, X-Caliber, Shillen, McGowan, etc. The cut rifled barrels you can get as prefits are marginally better, IMO when it comes to cleaning and performance. Any "prefits suck" comments are really only warranted at the highest margins of performance. The prefits are already better a factory barrels for cleaning. I have had Savage factory barrels that shot just as well maybe better than the prefits. But, prefits were easier to clean and you don't get as many lemons with prefits as with Savage factory. Lemons are rare with prefits.
You didn't say what action it is going on, but if it is A Zermatt/Bighorn or Nucleus, you can buy shouldered prefits that will come headspaced to your action. I use lots of barrel nuts, but a shouldered barrel is much easier.
I use Proof for my hunting rifles for the carbon fiber and for the precision from them. My match gun has had Shillen, Criterion and X-Caliber. All shot sub .5 moa with just a little work. I rarely can shoot better than about .5 moa. But, I have a friend who can shoot .25 moa with my rifles, lol. Unless you are amazing at shooting, then you probably won't notice a difference. Unless you are planning every edge to win the championship, then you won't notice the difference between the shooting of most prefits, IMO. No offense, but I say that especially because you are asking the question... I asked the same question out of ignorance, too. I hope that you quit worrying more than is warranted. Get a barrel and go shoot.