Re read my long physics thread for the right answers.
The barrel wont add any range, and itll only increase accuracy if your current barrel is bad.
The hop is whats going to make all the difference, and its easily transferrable between barrels unless you Rhop.
Theres no real "best" bore. But there are bores to stay away from; 6.01 and 6.23
You wont have the air volume to run a 6.23, and 6.01s foul too fast. 6.13 is even a bit big, but great for LMGs.
If you dont mind spending a bit extra, I highly recommend a PDI 6.05 or prometheus 6.03.
Barrel quality is the #1 defining feature of a barrel, so theres really no reason in cheaping out.
And for the record, hand-lapping a barrel to make it better is bullshit. You might get scratches out, but you'll never be able to maintain the same concentricity as a hone.