I would go Savage in .270, .308, or 30-06. The 30-06 will do anything on the continent with no issues(only say this because its the legal minimum to hunt wood bison with here). The .308 and .270 have about the same energy(slightly less than 30-06..not perceivable to the shooter really) but the .270 uses lighter bullets.
So if you want a one size fits all get the 30-06 and shoot 150gr bullets for coyote and deer and 180gr+ for everything else. The .308 is more or less a 30-06 with a shorter case and marginally less power(also used by many long distance shooters). The .270 will shoot faster and 'flatter' than the above mentioned as it uses a lighter bullet.
The 30-06 is probably going to have your largest bullet selection off the shelf. The .270 and .308 you should still be able to find everywhere included walmart/canadian tire etc but with a more limited selection.
But seriously they will all perform well...it's mostly what fits/feels good and budget(if you've handled a remmy and you like it..go for it). You can spend as much or as little as you like on a rifle and it will still kill things the same. Same goes for bullets. Many will piss about accuracy but any modern rifle will out perform the ones used by daily hunters back in the day. Same goes for ammunition. If your pride can take groupings of 2" at 100 yards that is....