I used a factory Tikka lite in a few matches where it was 10+ rounds in a few minutes, also shoot a few F class matches (obviously not competitively) and didn't have any notable stringing or group sizes going to crap.
Realistically unless it's a 223, something like light palma would be be the lightest you'd go. So Bartlein 3, 3b, 4 would all be ok.