Anything in .30-06 that's reliable. .45-70 is an overlooked choice, but it's also poor on anything past 150-200 yards without some serious "ballistic compensation.'' That being said, .45-70 will also stop anything on the continent. .30-06 was what I killed my first elk with, so I may be biased. There's always the .300 win mag, but forget about practice unless you reload. The .270 is a great round as well, and I have taken an elk with it as well. The problem with smaller calibers is bullet weight necessarily goes down. I shoot light for caliber 350 grn out of my .45-70 and mid-heavy 165s and 180s out of the .30-06. the .270 only likes 130 grn bullets in my rifle, so that's pretty much what I'm stuck with. The highest those go is around 150. That's a light-middle .30 caliber.
The most important thing, and I know this has been overstated, is shot placement. There isn't a bullet out there that you can miss with and still kill your game, unless you're talking prairie dogs and TNT bullets. My dad killed one with a 6mm that he blew up in front of the dog. The frag killed it.
Remington, Ruger, Thompson Center, and others all make great hunting rifles. H&R works for those of us on a budget. I own the H&R in .45-70. I figured if it was going to be one shot, it had better be a big one.