I'm going to throw another in the fire that will give you flat and accuracy with little recoil, and loaded properly should knock anything down to 500yards (assuming grizzly, African animals, and polar bear are not on the list). Just from what I have been reading, and from the possibilities in animals that can be harvested, I would consider the .243 Winchester.
It has bullets that will allow you to shoot paper accurately to 1000yrds. It will give you bullets to laser fire light projectile for annihilating varmints, and heavy enough bullets to knock elk down with it reason (200 to 400 yards). The only reason I say this (please don't beat me up for this), guys that live in the areas people drive thousands of miles for an elk use 243's and larger to harvest them at those distances. The other reason I am suggesting this is due to the fact that you want to be a target shooter at that distance.
Placing a shot in the boiler room of any animal with this caliber is going to drop it. Now for heavier game you will need to shoot 100grain class bullet for that distance.
As far as your choices are concerned, I would choose the .308. The reason I would is because that is what I did when trying to choose. Because you are shooting paper, you won't waste as much powder trying to punch holes, and when you need some punch you can load it hot and heavy. So, take your pick.
After some thinking another caliber that would be consistent in burn rate, usefulness as a target rifle, and won't break the bank in the reloading arena is the 7mmWSM. This would give you the hit of a 7mmRM and has a nice selection of bullets to go long range. 160 Accubond, 168 Berger, or 162 A-Max will accomplish all your requirements.
Tank