30-06 will work just fine, just try to get a solid bullet - Barnes TSX/TTSX or Hornady GMX, I find it's less meat wasted -less bloodshot- then SST, Core-Lokt etc.
Skinning is not rocket science, watch some videos, get a couple good knives and get at it. Good friend of mine told me fun ends once you shot, then the work begins. Words to live by.