I would recommend the 7mm Remington Mag. It's a great long range round coupled with the right bullet. With a Berger 168gr VLD (need a 1:10" or tighter twist, HSM makes an outstanding factory round with this bullet) it's got plenty of ummmph to drop a deer or elk as far as you can accurately shoot. It's also no worse on your shoulder than a 30-06, but in nearly any factory round configuration out-performs a similarly loaded 30-06, giving the shooter a little more slop in range and wind corrections and more downrange energy. Handloading is the same for the 7mm, but I assume with a first personal rifle you're not there yet. Both the Savage and Weatherby are fine facorty rifles. The Savage's action is great if you ever want to upgrade it with a premium barrel, there are barrel makers out their that make drop-ins for it that your gunsmith could install very quickly and easily (read cheaply). Teddy Roosevelt killed pretty much everything that walked the earth from North America to Africa with a 30-06, so with that said, either is an adequate round for your desires. If you get much larger of a case powder capacity and you might have to worry about building a flinch from recoil (assuming a lack of a
muzzle brake) and your accuracy and therefore your personal effective range are lessened. I'm not He-Man or macho about gun calibers, It's my opinion to get as large and efficient of bullet as you can comfortably shoot that will put the game down when it comes to a multi-purpose big game rifle. I don't like
muzzle brakes for hunting because they make it (IMO) intolerable to the ear of anyone around you including yourself (I don't wear hearing protection hunting unless I am staked out on a hill side and in the prone position, then the blast of a muzzle brake throws all sorts of crap up in your face), so that effects the caliber of rifle I shoot for hunting.