I hunt often with ARs. I also shoot a right handed rifle left handed. no problems. even suppressed. If you stick with mil-spec , it will have a deflector on it.
The biggest problems i have seen with the AR-10s , is that they are freakin heavy and not to many assecories. As they are not mil-spec most add ons will have to be from the manufacturer of the rifle. which means $$$$.
.223 with a Federal Fusion or a Barnes TSX will be fine for deer. Can go up to 5.56 and some heavier 75 grn bullets.
6.8 is an option but if you check ballistics not much different from 5.56 to justify the ammo cost of 6.8 spc.
the 6.5 Grendel is just outstanding. Ammo cost and magazine cost is alittle concern.
300 black out is a great new caliber. Actually all that is needed is a new barrel. Everything else on a 5.56 rifle can be used. Ammo is still alittle pricy, but should be more available soon.
American by birth, Southern by the grace of God.