Wheels come in different sizes, shapes, and durometers. Knowing what is best for you is critical in determining the right wheel.
Wheels are measured in millimeters. 50 mm is considered a small wheel. 51 mm-53 mm is average size. 54-60 is leaning on the bigger side. 55 mm is about the biggest "street" wheel you would typically want, but just about everything in skateboarding is more about personal preferences than anything else. Wheels bigger than 55 mm are typically for riding transition, vert, or for cruising/filming.
Durometer is a measure of hardness. More specifically, it's a measure of a material's resistance to indentation. The hardness (or...softness) of a skateboard wheel is identified by the durometer scale. The higher the number, the harder the wheel. Wheels usually fall in the 85-101 range. 101 is as hard as skateboard wheels usually get and are preferred for street skating, as harder wheels have less friction and rider faster . 99 is just a little softer, and is better for the skatepark. 98 and below is where the wheels begin to get gummier and softer, and are able to roll over cracks and pebbles better. This level of hardness is good for traveling by skateboard. A lot of filmers use softer wheels for their filming boards, not only so that they can roll fairly effortlessly, but also so that you don't hear them in the footage. Cruiser or filmer setups typically accommodate for softer, larger wheels through the use of riser pads combined with longer hardware to avoid the infamous "wheel bite."
Wheel shape is pretty simple. Generally speaking, there are two shapes. The classic shape is a more tapered shape. Conical or radial shapes are more squared off and provide more surface area.