The 7mm doesn't have that much bigger bullet to make much of a difference when compared to the .270, and the .270 Win makes a fine elk rifle as well. My recommendation on the first time purchase of a rifle for elk and deer is the .30-06 or .308 for your first choice and a .270 third. I don't know your experience with rifles but am guessing it is limited. The 06 or .308 will serve you well as an elk and deer rifle, and the ammunition will not kill your wallet either. If you are not very experience with a rifle you should be able to learn to shoot 06 or .308 well very quickly.
For elk I like the 180 grain bullet and it works well on deer. If you use 180 grain just about any factory ammunition will do as long as it shoots well in your rifle. If you go down to a 165 grain bullet you should consider a premium bullet like the Nosler Partition or Barnes TSX when using it on elk. With the .270 I wouldn't go any lighter than 150 grain premium bullet for elk.
As far as the scope goes I'd look into a good 3-9X40 with a duplex reticle just to keep things simple. Buy the best scope you can afford as good quality glass is worth it in the early morning hours and at dusk. I like a scope that will give 3.5-4 inches of eye relief, that way you don't have to worry about getting the scar.