Concur that for 5.56 use Barnes TSX bullets. I prefer the 62 grain if you can find it. I handload, so no problem here. 16" is fine. Longer barrel will not improve terminal performance enough to matter on deer-sized game.
But, even Barnes bullets are no excuse for exceeding distance limits. You should limit distance to no more than 150 yards, because retained energy drops too low after that.
I hunt with my Recce. It is built around Lilja's true Recce profile Navy M4 Recon barrel as spec for Crane on original Recce rifles. Might be a bit overkill for hunting.
Geissele SSA-E trigger. Leupold VX-R Patrol 3-9x40mm Firedot TMR scope. Offset Deltapoint Pro for up close. Daniel Defense free float rail.
This rifle is a precision build for out to 600 yards. I incidentally hunt deer with it too. Its capabilities at distance does not, however, make a 5.56 suitable at deer for more than 150 yards for sure ethical kills, maybe 200, but that's a stretch.
But, honestly, at 150 yards and in, any decent 16" barrel, a somewhat lighter trigger, any freefloat, and a 1-4x scope will do you fine.