Of course there is no way to know for sure how accurate any particular rifle is without shooting it but ARs can be very accurate. I have an 18" barrel AR that I put together for less than $1000 that will pretty regularly do MOA (1 inch at 100 yards). I do tend to buy match ammo, but I think that the particular batch of surplus ammo that I have been using in that gun was all it took to get MOA accuracy. But to be sure, ammo makes a big difference in accuracy. Consistency is the key and cheap ammo often lacks the carefully controlled manufacturing conditions and testing necessary to get that consistency. But from time to time one does find a cheap batch of ammo that surprises and shoots as well as the expensive stuff. There is also an aspect of barrel harmonics (includes the entire rifle, and the shooter, actually) so that a particular type of ammo that is great in one gun might shoot badly in another. It is not actually possible though for inconsistent ammo (ammo with widely varying primer, powder and bullet characteristics) to shoot well in anything, at least at long distances.
The general consensus is that Federal Gold Medal Match ammo is the best of the bunch, so that is what I would try if I didn't want to experiment with a bunch of different brands. Make sure you pick a bullet weight (actually bullet length... well actually it's even a bit more complex than that) that is suitable for your barrel's rifling twist rate. A 1 in 9 barrel will generally work with ammo up to 69 grain, 1 in 8 will handle pretty much anything, as will 1 in 7. It is true that you don't need a 1 in 7 to shoot light ammo (like 55 grain ammo and lighter) but it will shoot accurately with that twist (there really is no such thing as an over stabilized bullet.)