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.)
Here is an inexpenive and effective deer feeder I made recently.
No batteries to go dead, no hoisting it up in the tree, plenty of capacity, very easy to fill - so far, I love it.
I have made two of these and they are easy to build.
An empty 55 gallon drum, some 2x4's, some PVC tubing and fittings, a little bit of hardware and some paint - and you are ready to go.
I designed it so you can stand on the lower rung and fill it - the top is about 6.5 feet above the ground.
It holds about 375...