I've used my Remington 700 BDL in .308 for everything, for years, using one single load - a 165gr Sierra Game King HP loaded to 2650fps, which roughly duplicates the performance of M118LR that I used in high power competition for years. I limit my shots depending on what I'm hunting, but I know that load and what that load is going to do. My last Elk was a big cow at 350 yards, and even at that range it put her down on the spot. But I hit her in the right place to do it.
7.62x54R is a full power load, equivalent to a .30-06 and with the right bullet will work just as well if you have the sights to do it. Same with 8mm Mauser.
I know Colorado law says that 6mm is the smallest that's legal, but the thing I think a lot of people don't think about is their shooting ability. Sure, it may be legal to shoot an Elk with a 6mm but if a person's ability isn't up to the task all you wind up with is a wounded animal most likely going off to die a painful, lingering death. I would say the smallest caliber I'd feel even close to comfortable using would be a 6.5, and even then if I was using a 6.5x55 I'd keep my shot closer than if I was using my .264 Win Mag. I think 7mm is the smallest most people should consider, and .30 would be better. I think your choice of an '06 is a good one, and you're right - you can get ammo for it everywhere. Same holds true for the 7mm, but the 7mm-'06 argument is just like the 9mm-.45 argument - everyone has their own opinion.
Best thing is just as jmg8550 said - Know your rifle, know your cartridge, and know your limits.