I haven't seen a bull barrel, but it's the AR world, so I'm sure someone makes it. I also haven't needed any extra weight on my 10.5" pistol.
Are you buying it built or building?
Buying complete: BCM, PSA. Both solid, both with good reps. PSA will be a little cheaper, BCM will have better components. Both will work.
Building: that's a deeper question. I yet a YHM slimline handguard, mils per upper I already had, sourced the small stuff (forward assist, delta ring) from midway, and the barrel and BCG from MAS defense. I had no issues with my stuff. But the sky is the limit with AR parts.
I would recommend carbine gas system, and no less then 10" barrel. Also I know you have the receiver extension, but KAK makes one for the sig brace that let's you run a carbine buffer and spring. Helps with reliability.