These threads are very common, must be a lot of people heading out of the cities.
In regard to bears in NM, southern UT, a .40 might be an overkill, they are small. Even in the Lasal Mountains SE of Moab, they are more frightened of you than you will be of them. After l living in Moab for over six years, and hiking in the Lasals the bears were never a problem; unless you left the food out at night, and then it would disappear at night. And the bears in the mountains of western CO and Northern NM are small (at least compared to the biggies up here in Idaho, WY. MT).
In fact, camping years ago outside of Colorado Springs at the WYE campground, I had two walk into my camp and simply setting off the seven stage alarm on a Hummer got them running down the trail looking like they were not going to stop till Montana. Noise works. And after coming head to head with grizzlies, spray works great!
As for mountain lions, a .22 would suffice
if you see it first. I have run across them a few times, and three rounds in the ground in front will get them running in the other direction. Problem with a ML is if you don't see them until they are on you, at which point the gun might be a club. Best to stay Bear/ML aware.
As for where to see a ML, sometimes it is as simple as viewing a trail cam in your backyard...
View attachment 990600
And another thing I didn't think of till last week is there are other dangers out there in the woods. There are bigger animals just as dangerous if startled.
I walk my dogs every AM around 3-4AM and last week coming around a trail I walk on quite often, out of the trees to the right came a very large moose and she did not look happy. My 150 male Malamute got it running, but that was questionable for a few seconds. I should have thought of this many years ago. There are not the animal to attack, kill and eat you, but a 1000 pound cow peed off coming at you will do you in just as fast as a ML. And if it is a 1400 lb male...say goodbye.