very trueYOU are the reason the gun will be accurate,practice often .All the big names are fine you need to go to a gun store and try them.hold them see how they feel imagine lugging it around the position of the safety what type of hunting you do are all things to consider its a very personal choice.most gun owners have more than 1 gun
also, try to stay away from the Rem 770, i heard they are accurate but they are junk.. most i found agree with this opinion.
One of the most accurate rifles i have seen is a savage mod 11 in 308 win. a buddy of mine has it and he is getting on average .6 moa with it a 100 yards. He also shot a group roughly 1.6 moa at 200 yards, but that was a rough extimate, and with handloads.
like the saying goes, buy good once or cheap twice.
As mentioned, a 30-06 will do nicely for what you said. A .270 win would work too, but you are somewhat limited on bullet weight, as the max ive seen in a factory load is 150 grain. You wont notice a difference in bullet drop probably till 350-400 yards and even then its slight. Good bullets for deer are in the 150 to 165 grain range. Good bullets for elk are 165-180 grain, and possibly premium. And i daresay since you are a new hunter you dont have any business shooting over 250 yards unless you put in the range time.
Best of luck and always be safe,