better 5 lbs off the old gut than 1 pound off the rifle.
if you are just going on day or overnight trips, the weight of the rifle shouldn't really matter... now if you are packing in for a week, go light on everything (except binoculars). break your toothbrush in half, take chlorine tablets instead of a water filter, leave the cotton towel at home and bring a vicose one, repackage your food in ziplock bags. skip the "cookset", bring one pot and eat of out it.
caliber, something from .270/7x57/7-08 to .300 winchester (long or short) should do just fine.
and please, don't shoot a sheep with a plastic rifle.