RE: WHAT IS THE BEST CALIBER....
scope eye - You don't give us much to go on...please define "mountain hunting" and it would make things a bit easier.
The only thing you really describe a need for is long-range target shooting, small game and varmints. These applications scream ".223" or ".22-250". Of these, the .223 probably represents the most value in terms of ammo costs.
If you're going to throw a bit of deer hunting in the mix ("mountain hunting"?), a step up to the .243 would be logical.
If deer hunting is equal to varmint control, then a .25-06 or .257 Roberts are fine dual-purpose cartridges.
If deer hunting is a priority, then start with the .25s mentioned above and include the .260, 6.5x55, .270, .280, 7mm-08, 7x57, .308 and .30-'06 in your search.
If you might take on something a bit bigger than deer, start with the .260 mentioned above...and keep going on up past the .30-'06...