Quote: I'll be hunting primarily in southwest: Arizona and New Mexico, for sure, and perhaps Colorado and Texas.
You can get a lot of area info from your local game warden or fish game person.
I'll address only the shooting aspect of the hunt:
Get a gun you can handle and be honest about it. No sense of trying to be macho about it, you'll be doing yourself and your quarry a disservice.
For years now, I've hunted with (mostly) one rifle:
Winchester Model 70 (in .270) with a 3X9 Burris Scope
I've shot deer (mostly) from the woods of NY/VT, to the desert southwest;
Practice Practice Practice! I can't stress this enough! Since you'll be hunting primarily in the southwest, you're going to have some long shots Being that said, you'll need to know your limitations. If you can only hit targets consistently at 200 yards, then that's your limit - period.
For example - Here are two deer I shot in AZ years ago, one (on the right) I shot at 50 yards. I was climbing up a ridge to get into a classing position when I came across him. I had to shoot off-hand, cause there was no time to get rest. The other one, I shot at 350 yards and I had all the time in world cause he was chasing does (he never knew I was there-until the bullet hit him!)
Why was I able get both of these deer, yup practice-practice-practice!
Finally - Know the anatomy of you quarry, generally in or behind the shoulder has served me well.