Ruger .44 Rem Mag first pistol I might buy...

The "Rem" in the cartridge designation is short for "Remington" the company who designed and brought out the cartridge. As others have said, starting with a 44 mag is kind of like jumping into the deep end of the pool on your first day of swimming lessons. Most would recommend stating with a 22 LR to gain proper technique and then going for a bigger gun. If one were going to start out wit a centerfire, a .38 Special would be better as the recoil is much less than a .44 mag, ammo is pretty cheap, as are decent guns. Buying a .357 mag would allow you to still shoot .38 Specials as well as more powerful .357 magnum. As a starter load in the gun you are thinking of, you may want to look at shooting 44 Specials in it. These do not have as much recoil, cost less, and would be better as a beginner's load than any commercially made 44 mag round that I'm aware of. If you are planning on using the gun this year and getting as late of a start as September, I would strongly suggest hiring an instructor to shorten the learning curve. This would be my advice in any event but it is even more so the way you are going about it. It is much more difficult to gain adequate proficiency with a pistol than with a rifle and the few months between September and deer season is not enough in my opinion. A sportsman owes it to their quarry to be able to make a humane kill rather then let the animal go off and suffer.