I have to agree with Ridgerunner. I've had the fortune to shoot a lot, over the last 20 years, have punched around 70 big game tags, and shot around 600 deer and pronghorn on the job (mostly cripples).
I bought a .300 Win mag, and sold it because it was causing me to flinch. My 7mm Rem mag is the upper limit for me, and has done very well on longer shots on tough game (270 yards to kill my bighorn, a couple elk at 275-300 yards). My .30/06 is my favorite deer/elk gun, 2 one-shot kills this year, 175 yards on a big mule deer and 120 yards on a pronghorn. In the past, I've killed everything up to bull moose with it; the only one I had trouble anchoring was a mountain goat billy at 150, but they are notoriously tough. I'm 5'8", 200lbs, stocky muscular build, but the big magnums aren't for me, because I think about the gun instead of the target, and that's the beginning of bad shooting habits, IMHO.
VERY, VERY few hunters can shoot proficiently beyond 350 yards. If you can't, and aren't going to make the commitment in terms of time and money to shoot that big gun a bunch, you have no need for it. BIG MAGNUMS ARE NOT A SUITABLE SUBSTITUTE FOR SHOT PLACEMENT!!
My pick for what you describe would be either the 7mm mag or .30/06; but if I didn't enjoy shooting it, I'd go smaller. For a very gentle shooting round with impressive terminal ballistics, I'd recommend a 6.5mm Swedish Mauser; probably 1/2 the moose killed in Scandinavia every year are shot with that caliber.