The LR/AR-10 platform doesn't have the same "like legos" continuity across brands like the AR-15 because there isn't an a standardized spec for them. So, I'd advise going with the same brand of upper and lower, and potentially even handguard.
All of this said, I've got a .308 built on Aero receivers that is very accurate, so you certainly don't need to spend the big bucks to hit your target. What's more important (assuming the other parts aren't junk), is the barrel and trigger.
If you are building it yourself, I recommend checking your bolt for headspace, or better yet buying a barrel that comes with a headspaced bolt.
I'd only go the piston route if it were known/really good quality parts, preferably purchased as a complete upper, and/or with an adjustable gas system.