Many Choices.
Hey.
My first handgun was a GP-1000 4" .357. I sold it so I could get my Beretta which I love, but do miss the good ole' Ruger.
I agree with many that a revolver is probably the place to start. If you are going to be hiking a lot in that dry NM heat and sun I would suggest something you'll be sure is always on you. I would suggest a Ruger SP101 or a Smith and Wesson Model 60. I would load both with hollowpoint .38 +Ps from any goood, brand name ammo company. I like Remington Golden Saber and Black Hills ammo...it's just a personal thing.
I would practice with it regularly shooting standard practice loads (CCI, Winchester White Box, UMC). With all that land and hills I am sure you won't have trouble finding a place. Bring a friend and have a good time.
Over time, I am sure you will want a few more guns. I wouldn't suggest a single action .45 ACP as a start up gun (Kimber, Colt, Springfield, ParaOrd). They require a lot of practice and time to get good and comfortable with. I would suggest you look at autopistols. I will second the Glocks. I love my Glock 19. Also check out Sig Sauers. They are very sweet and reliable. I would also consider a .22 LR either handgun or rifle, just to have around and for plinking. You never know.
Also, consider what leather you are going to go with. A good holster is sometimes much sweeter a purchase than the gun...only because if you get a crappy holster, carrying the gun won't be any fun at all and you won't enjoy/respect yourself later. Get good gun leather. Haugen, Galco, etc are all great places to look....but there are so many more.
Get books on shooting. Defensive shooting, home defense, outdoor, hunting, read all you can read and talk with as many people as possible. It's good to make friends at the gun shop and on the range. That "stigma" will go away in minutes and you'll realize that there should never have been that stigma in the first place.
I guess this is long winded, but I grew up with no guns around me except on my grandfather's farm. I love my country and the freedoms it allows, even though some disappear from time to time. Owning a gun is a good thing and a responsible thing for yourself and society if any harm should arise. So again, read up, talk with others, practice, pick good leather, and get a gun that fits your hand well!
Good Luck.