With regular ammo, consider a 234 Win or 7mm-08. Reduced Recoil Ammo will also work for deer: 270 / 308 Win, or 30-06.
Conversely, in training my wife and sons, I used a 30-06 with Reduced Recoil loads at the range and substituted the real stuff in the field. (They'll never know the difference with their heart pumping and a deer in the sights.)
Want a quick and inexpensive call for Moose? Take an empty 32 ounce coffee can, and make a small slit in the bottom, only about a quarter inch. Then, take one of those really big red rubber bands, the ones that go around big folders. Cut the rubber band to make one long piece.
Now, thread one end of the band and tie a knot on the outside of the can so it won't pull through. Cut the band off on the other side so it is even with the top of the can.
Now, wet your finger,...