Welcome to HF. No matter which way you go, mobile or base station, most all of your resources (money, effort, etc) should go into your antenna. A rule of thumb is the best antenna is the one with the most aluminum in the sky and as high as you can get it. To help choose a commercial antenna, go to www.eham.net
. In the reviews section, you will get comments from other hams regarding the pros and cons of just about any ham gear you can imagine. Also, I would stay clear of 10 meters. Openings on 10 meters are few and far between due to our current sunspot numbers. 10 meters is a fun band (when it's open) and 10 meter antennas are small and easy to pack. Currently, the workhorse band is 20 meters (17 meters is a close second). But the physical size of 20 meter antennas make them a pain (20 meters = 66 feet!) in the rear. A good mobile antenna brand is HI-Q but at $500 and up they are out of reach for many. You get what you pay for and like I mentioned earlier, most of your system's cost should be in the antenna. Have you considered homebrew? When you build your own antennas you learn quickly what works and what doesn't. I like Dave's idea of not operating while driving but rather set up your temporary station when you get to a good spot. In Moab that might be a high spot on the trail. Good luck.
1991 FJ80 converted to an HDT with an A442, Safari intercooler, 3" exhaust, factory Toyota subtank, 3" lift, 285's, Warn 9500xi, rear drawer system, 42qt Engel fridge.