Barrels aren't guaranteed to headspace. I went with the Criterion Hybrid. The Brownells BCG I got didn't work with it. The Armalite pattern BCL BCG did work with the Criterion bbl.
I ordered a Fulton Armoury bolt because Criterion uses FA bolts to headspace at factory. I have a better chance with a better match.
Bbls are hit and miss with what works in combination with a BCG or what bolt headspaces best.
The Brownells BCG fit with the BCL bbl just fine.
If I were you, and I was going right from scratch with this, consider not only what BCG/BBL combo you're doing, but also in conjunction, an Adjustable gas block and what buffer/buffer tube combo you'll use with those.
Choosing all 4 that will make for one flawless gas system will likely be better than choosing the BCG/BBL, and then later piecing together the rest, only to find out it is short stroking because of Low mass or improper buffer etc.