Aager,
Shoot a full box of 7 Mags, 175 grains, from a bench, and your love affair with it will be over.
Of the preferences you mentioned, I would go with the .270. You won't be sorry.
Also, if you really want a nice round, research the .280 Remington. You will find that it is right up there in power, near the 7 Mag, without the undue recoil and blast.
Unless you are a pure Elk hunter or Moose hunter, there is no reason to own a 7 Mag.
By the way, if someone lets you hunt on their farm, and they hear that 7 Mag go off, they will never invite you back again. Incredibly loud cartridge.
Best, Mannyrock