My personsal choice would have to be the 243.
Reasoning:
I would be doing more 'yote shooting than deer, necessates the more rounds shot for varmint, faster 55-85grn loads. Means more money spent, but cheaper than buying rounds for the bigger weapons.
2nd. You can play with various loads, if you reload or know someone who does, to find 2 loads that will print very close to the same sight in characteristics, less scope adjustments when the time comes to use the same rifle. May find a load in the upper weight range that will double duty.
I would personally stay to neck shots with the 243 just for the fact of you will be shooting larger bodied deer and no need to ask a lighter weight/design bullet to do what something twice its weight could be doing.