RE: Help with Rifle Selection.
Good choice on the .308, I happen to be a Browning fan so there's my choice...
I personaly hunt with a scoped .270 OR for stalking, I use a .30-06 with open sights for some of the same reasons your looking for.
I chose the .30-06 for the bigger loads available (220 gr.), in case I ever went Moose or Elk hunting, then I can cross dress it a little bit better than the .308.
You did say another all around round, so that's my opion.
Also, I have hunted with a Winchester .30-.30 and this does just fine. Really any .30 cal is good, but the .30-06 gets you a little bigger load if desired?
Another note, the recoil of my .30-06 Browning BAR is minimal with the gas operated system, noticably less than the .270.
Lastly, the BAR is very light and a joy to carry all day long, with the chance of jumping and shooting at a buck in brush @ 20-30-40 yards and needing another quicker follow-up round. This was the case 3 years ago when using the semi-auto, as I tagged the buck instead of watching the famous whitetail run away.