Really speaking, assuming the barrel has a consistent polish on all surfaces and isn't bent, then it will shoot straight.
Then you have varying degrees of prting, which may or may not make a barrel quieter than another.
Then you have the bore size and how it matches to the paint.
Some people swear by a large barrel like a .693 as generally nothing will get stuck, so you won't get breakages that way. If you were a front player, this could be applicable.
So your accuracy would really come from how round your paint is, then, how well it fits your barrel for consistent shots.
This is why multiple back sizes were introduced, so that you could match your nice round paint, to a barrel.
I had a Redz barrel set and it was very nice. 5 backs and 3 fronts.
I sold that with another gun and have an SL barrel kit, also very nice.
They are about £100 new, so see if you can get one second-hand or perhaps as has been suggested, try a Unitec or Redz etc.