Savage makes fine rifles. Let no one sway you from buying one.
For "long range" targets, regardless if your speaking of paper or game animals, almost any of the larger calibers will do nicely. Start with the .243 Win, or 7mm-08, or .308 Win. Those are all fine short action calibers. If you want more flexibility in terms of the range of bullets weight available (think a wide variety of game, i.e. antelop to moose) , then a long action caliber may be a better choice. The most common are the .270 or .30-06. Both are top notch performers and are able to really reach out.
You can make your choice as complicated or as simple as you want. I suggest you buy a Savage rifle in .30-06, and find some ammo with a 150gr soft point (or other such performance bullet) and head to the range and **LEARN** your rifle. After a few dozen rounds and after a number of shots on targets at ranges from 100 to 400 yards, THEN get serious about what you want to do.