I'm going to agree with nearly everyone else and say you can't go wrong with the 7mm-08. It's inherently accurate which comes from it's .308 lineage. It's hot enough to provide all the knockdown power you'll ever need on any deer that walks. And finally, the recoil is light enough that even recoil sensitive people shoot it with little concern.
I've shot a whole bunch of deer over the last 10 years with my Browning Stainless in this caliber and never had to shoot a deer twice.