From your initial post, you only have two choices, the .243 or 7mm08. Cartridges like the .260, .257 Bob, etc aren't readily available and cost a fortune compared to standards. The LA rounds are going to be a handful to someone who is recoil sensative.
A .243 with 90-100 grn bullets a proper shot placement will drop any whitetail or pig around. Step up to a 7mm08 and you can do a bit more. 120grn bullets will drop whitetails and shoot relatively flat. 150grn bullets mimick the performance of a 165grn in a .308 and are flat devastating on pigs and wood goats. IMHO the 7mm08 is the perfect whitetail deer round for nominal responsible shooting ranges 99% of hunters encounter.