Alexander Arms, they are going with their own barrels, but it might be a slight wait to get one. Templer Customs, Britlein barrels with a good reputation. Loki Weapons does good barrels, Les Bear will do a good cut rifling stainless barrel.
You can get a cheaper button rifled barrel that might shoot pretty good, but if you want a really good barrel, go with cut rifling.
Gunwritr recommended Alexander and Les Bear. I respect his opinion, so I would say you can't go wrong with either one.
As for accuracy, I have seen a lot of pictures of 1/4" groups at 100 yds with factory AA ammo. With good ammo, a Grendel is as accurate as a semi rifle can be. Which is pretty accurate.
Edited for spelling, I suck at typing.