There are some fine 7mm rifles out there, for a new shooter, I would recommend advoid anything labeled "magnum".
As I read your post, you are talking about 300, 400 yard shots. If this is your first hunting rifle, you may not be a very experienced shooter, and even with good shooters, 300 to 400 yards is a very long way.
What ever rifle you get, practice with it. Try shooting it in unsupported positions, like sitting. Shoot on paper using a target. Don't shoot at rocks, the dirt splashes make you think you are close, but actually, you are not.
The distance you can keep all your shots on something smaller than a dinner plate is the maximum distance you should be shooting at game. You owe the animal a quick end. For a new shooter that may be 100 yards.
I have always been partial to the 30-06, logistically it is hard to beat. So many choices, and they are easy to find. But if you like 7mm, a 280 Remington is a fine cartridge. The old 7X57 is a fine cartridge, just a little less horsepower. Just advoid a 7mm Mag, too much noise, too much recoil. Takes a lot of practice to control those things.