Minimum would be a 375Rum for deer. Every barrel maker would vote for the 300Rum. More work coming in down the road. Why do you think that they sell powders in 8lb. cans?

They are both more than you need. A 30-06 will do all that just fine. My 270 Win will do just as good on all but maybe the moose. With a good premuim bullet it should work there too.