I second the motion for the .243. The .270 and .308 recoil nearly as much as a .30-06; the .243 is noticeably milder, and is very effective on deer (now watch this last statement start a debate!)
I have a Winchester Model 70 Featherweight and it is a joy to shoot. Once I floated the barrel and lightened the trigger (did this myself) it turned into a tack driver, provided I let the barrel cool a bit between shots. It is easy to carry too. You might look at one of these for the smaller folks in the household.