This is one of those impossible to answer questions. There are many factors that could enter into one's decision as to the best caliber for short action and long range. If all you care about is the ability to hit a paper target at the maximum possible range with the least bullet drop then the decision is very easy, just look at the ballistics of the cartridges with the bullets you would use. But if you want to consider cost of ammo, availability of ammo, availability of ammo components (bullets, cases, etc.), the availability of reloading data, the energy in the bullet at a particular range, etc., the decision become much more complex (as well as subjective). For example, 22-250 or 220 swift might be the best possible choice for flat trajectory out to several hundred yards, but it surely isn't as powerful as .308 at 500 yards (or any other range for that matter). Many people like the .223 for it's low recoil, and wide availability, and some people even use it successfully at 1000 yards with very heavy bullets, but I doubt anyone would claim that it is the best. .308 is probably the best possible choice from the point of view of cost and availability, but some people find the recoil to be too high (while others use a 50BMG for long range), and the trajectory way out at 1000 yards and beyond is certainly not the flattest of all short action cartridges.
Decide exactly what you want to do with the rifle and what your budget is (in time and dollars) and then you can make a rational decision on cartridge. I once saw an article where the author looked at the overall cost of owning a long range rifle. He found that if you included the cost of ammo, required to stay good enough to actually be able to shoot long range, that the ammo cost was several times more than the cost of the rifle and barrels (I think he figured the barrel life at 4,000 rounds).