Tires, Wheels, & Pressure For desert running, you're not going to need a very aggressive tire. An all-terrain of some sort would be your best bet. For a more purpose-built tire you should look to something like a BFGoodrich Baja T/A or a Goodyear GSA. Both these tires are made for desert racing and have thick sidewalls that will better resist punctures at high speeds.
Depending on whether or not you have a fullsize truck, you'll want to go with tires ranging somewhere between 33 and 37 inches tall. You don't want to have tiny donuts that'll get sucked into holes and ruts, nor do you want huge diggers to lug around. You want to keep your unsprung weight (the weight below the vehicle's suspension) down so as not to break components or distort the suspension's intended ride.
Wheel choices are left open to you, the builder, but the sport has been moving aggressively towards 17-inch rims with bead locks. The bead locks will make sure your tire doesn't separate from your wheel when your tire takes on lateral force.
Pressure should be kept at around 15 pounds or more. You do not want to have too low a pressure because of the higher speeds you will be reaching compared to other forms of off-roading. Bead locks will allow you to go to lower pressures than a wheel without bead locks.
Suspension & ShocksThis is what makes a desert truck a desert truck. You can have all the power you want and the best drivetrain and tire combo possible, but you ain't gettin' over 40 mph without a supple suspension. Obviously an IFS or Ford twin-traction beam (TTB) setup is going to give a better high-speed ride than a solid front axle if you're talking stock suspension versus stock suspension. The TTB Ford has been known for years as a great, easily modifiable suspension that can provide you lots of travel, so this would be a great starting point or even great as a swapped-in unit. An IFS rig can make a great choice if you just want to bolt on a lift and go. Two-wheel-drive IFS trucks are tons of fun and make great jumping rigs. For a four-wheel-drive IFS truck, though, there are very few kits on the market right now that will add any travel to your suspension. Hopefully that will change someday soon, but in the meantime, you're limited to the amount of travel that you have in stock form. If you have $50,000 to drop on a custom IFS front end, then nothing is going to catch you in the whoop-de-doos. But if not, then it is much easier to work with a solid axle.
For those of you with a solid axle (which most all of us have in at least the rear), you can gain travel and achieve a better ride by tuning your suspension. If you're on a budget and have a leaf-sprung vehicle, keep the leaves. If you can't even afford to buy some prerunner leaf packs, you can tune your leaf pack to your liking by adding or removing a leaf or two from the pack. Your truck probably has an overload spring on it, so try taking that one out first.