Remington Mag? Weatherby Mag? Winchester Short Mag? Remington Short Action Ultra Mag? Reminington Ultra Mag? Other? There are differences between all of them (some major) and ammo is NOT interchangeable. Some will actually chamber rounds for the others, which can be VERY dangerous if fired! I'm going to assume its a run of the mill 7mm REMINGTON Mag as they are the most common. If so it is a decent all around big game round. Good for everything from small whitetail sized game all the way up to elk, moose and brown bear. Heck, you can even load up some lightweight, hot loads for coyotes and stuff. Recoil in most rifles is moderate, even with heavy loads, and can be handled by most adult men without an problem, but it varies on factors such as the weight of the rifle, how that rifle fits you, loads you're using, position you're in, your personal tolerance, etc. I'd say if you're comfortable with a .30-06, you won't have a problem with a 7mm Rem Mag.
As far as I know you can't hunt deer with a .22 in ANY state. I know a few states allow .223 and up, but never heard of any allowing a .22LR. Even if it were legal I wouldn't recommend it at all! Far too much margin of error.