You should consider wheels only after you've chosen tires. Generally, larger is better for off-road driving, but it's the weight of your vehicle that will determine the tire and wheel sizes for your vehicle.
After you settle on a wheel size, you need to think about composition. There are two basic choices: alloy wheels and steel wheels. In alloy wheels, aluminum is the predominant metal, which makes for a lightweight wheel. The reduced weight helps your vehicle get better mileage and puts less strain on the bearings and other parts. But alloy wheels aren't as sturdy. A good collision with a rock can break the wheel, which may be difficult to replace when you're in the middle of nowhere. Steel wheels offer greater strength because they feature large amounts of iron mixed with carbon and other elements. The added strength of steel wheels will cost you more in terms of mileage and wear and tear, but they are more practical in off-road conditions.
You might also consider a bead-lock wheel if you're going to air down your tires a significant amount. To understand why, it helps to understand how wheels and tires work together. On a normal wheel, air pressure pushes against your tire's bead, a ring of steel wire shaped to wrap around the rim of the wheel. As pressure increases on the bead, it presses against the lips of the wheel, keeping the tire firmly attached. As pressure decreases, so does the grip of the bead. Air down too much, and your tires can spin on the wheel or, worse, peel completely off.
That's where external bead-lock systems come in. External bead locks feature a ring that clamps the outer bead of the tire to the wheel with a series of bolts. Some bead-locks use eight bolts, while others use 32, 36, even 40 bolts. The number is significant because you need to check bead-lock wheels regularly to make sure the bolts are tight. If you have a 32-bolt system and five tires (including the spare), you'll be checking 160 bolts!
As you can see, you must put a lot of thought into the wheels and tires you buy for an off-road vehicle, but other big decisions still await you. On the next page, we'll look at the many options available for off-road suspensions.