Let me start by saying my choices are based mostly upon my hunting expierence. I've been hunting for about 35 years, mostly deer. I've taken quite a few hogs and a few varmits. I have found that larger bullets just tend to work better. I keep my shots under 250 yds and have no need for super fast magnums.
I have used my 6mm Rem in the past and was not impressed with it's performance on deer. For me it is a long range varmit round right beside the .223. I'm not trying to start a caliber war, just answering the OP's question as to my preference.
I know it is old school but I prefere larger, slower calibers. For hunting I tend to carry a .308/30-06 most of the time and a .45 for SD. JMHO.