For a quick and easy answer to what kind of wheels to get, most skaters will be happy with wheels from 52mm to 54mm, with a hardness of 99a. Also, check out this list of the best skateboard wheels. But, if you want to give it a little more thought, then first ask yourself what kind of skateboarding you think you'll be doing:
Transition / Vert
Larger skateboard wheels roll a lot faster, and when riding ramps this is what you want. Try 55-65mm size wheels (though many ramp skateboarders will use even larger wheels -- try something like a 60mm wheel first, as you learn), with a hardness of 95-100a. Some wheel makers, like Bones, have special formulas that don't list durometer, like the Street Park Formula.
Street / Technical
Skateboarders who like doing flip tricks often like smaller wheels, as they are lighter and closer to the ground, making some skateboarding tricks easier and faster. Try 50-55mm skateboard wheels, with a hardness of 97-101a. Some brands, like Bones, make special Street Tech Formula wheels that also work very well, but don't have a hardness rating.
Both / All Terrain
You'll want something in the middle, with slightly softer skateboard wheels. Try a wheel size 52-60mm, with 95-100a hardness. This should give you a balance between speed and weight.
Cruising
Usually cruising wheels are much larger for speed (64-75mm) and much softer for riding over rough terrain (78-85a). Other wheels for cruising are available, such as huge dirt wheels with knobs, but these aren't recommended for skateboards (try longboards or dirtboards).
