I have used four sets of B.F. Goodrich All Terrain T/A tires and have never had a flat. Slow leaks, yes (10psi per day). But not a flat tire. I had these on two trucks, a 1996 Chevrolet S-10 4WD pickup and my current 2002 Toyota Tacoma TRD 4WD pickup.
Any premium LT rated all terrain or mud terrain tire is mandatory in my opinion. And look for 3-ply sidewalls. Not all so-called off road tires have that feature. It will make the difference between swapping out your spare tire in the field or driving home after a wonderful day on the trail.
All Terrain tread should be more than adaquate in southern Nevada, as the soils are granitic and don't hold moisture (i.e. mud) like the gumbo we get in northern Nevada. Before I moved to Winnemucca, I did most of my wheeling in Death Valley and the eastern Sierra Nevada and west central Nevada where I lived for over three decades. In the northern Nevada gumbo mud, mud terrain tires will be my next purchase, but you can't beat an all terrain tread for general use (the tread blocks on all terrain tread are not far enough apart to allow mud to be flung off at low speeds, thus they pack up and turn to slicks).
All terrain tread is relatively quiet on the street, great in snow, and for 95% of the off roading you will encounter. Not sure of the deep, loose sand, but I've wheeled in soft soils and sandy stretches without issue. That's why I lower my air pressure to around 15psi. And lowering your air pressure makes those sidewalls more vulnerable to attack, thus the necessity for 3-ply sidewalls. Lowering your air pressure also protects your tires to sharp rocks, because they then mold themselves over the rock instead of put a hard face to it; thus protecting the tire by not allowing the sharp rock spearing it through. Lower pressures mean a better ride over washboards. And it's a traction aid. BFG's generally chunk their blocky tread if you run them off road at street pressures, but seldom do at low pressure.
My BFG's take a beating and always bring me home (there ... I just jinxed myself ...
). I don't even bother to air up when I hit pavement ... I just blast away at 65-70mph for miles on end and air up with my shop air compressor instead of sitting on the roadside for 45 minutes waiting for my 12v compressor to put 20 psi in each tire. The tires don't warm up appreciably even in summer. I just take the curves a bit slower due to the fact that the tires are more flexy.
I learned my lesson on tires with my '96 Chevrolet S-10, which came from the factory shod with Goodyear Wrangler RTS tires. I think RTS stood for "Really Thin Spare." I had 10 flats and one destroyed tire before I put on the BFG's. Most of the flats were rock punctures caused by gravel from maintained dirt roads stuck in the tread working their way through the carcass. The destroyed tire was caused by a 1" square stone that sliced open the inside sidewall like a Ginsu knife.
My Tacoma has 16" rims, I run stock size LT265/70R16 or 31" and change BFG's. They have the 3-ply sidewalls, 8-ply tread. They're not cheap, my last set was purchased in the spring of 2007 for nearly $925 total. They've got about 35,000 miles on them, or about halfway through their tread life.
So, to make a long story short, I'd purchase a good set of LT rated tires at minimum whenever your funds allow. Because you're going to keep the others in the group waiting and/or working while you swap out your current tires by the trail side. And I hope you brought more than one spare ...