There are so many wheels to choose from, and no single wheel that's going to work for all people, and for that matter, there's not even a single wheel that's going to work for a person on all surfaces. Just understand that there are four basic specs for wheels: diameter or height, width, durometer or hardness, and hub. Understanding these specs pretty much unlocks the mystery of wheel shopping, and lets you decode what any given wheel will do for you and your circumstances.
Diameter (height)
The typical diameter of a derby or quad speed wheel is 62mm. Quad art wheels, just for comparison, are typically shorter than that; and for further comparison, inline speed wheels are very tall. These are very different wheels, but they serve to illustrate the general principle: a bigger diameter (or taller) wheel gives a longer roll and more power or speed, and a smaller diameter (or shorter) wheel gives a shorter roll and more maneuverability or agility. So inline speed wheels are the fastest, you pretty much stick to the long track and skate fast. Derby wheels still allow for speed around the short track and also for quick maneuvering through the pack. And art wheels are the most agile, the better to do all those fancy moves with. But as I said, that's just to illustrate the general principle; you're not going to swap between inline and derby and art wheels; there are only a few derby wheels taller or shorter than 62mm, and it's not something that you have to think too much about.
That said, there are taller outdoor wheels—e.g., Radar Pures are 66mm—where the longer roll helps cover more distance. And incidentally, taller diameter wheels also provide a smoother ride for rolling over pebbles and twigs, or Tootsie Rolls if you're in a parade.
And also, there are a few shorter indoor wheels—e.g., Radar Tuner Juniors and Atom Jukes. Tuner Juniors were originally developed for kids, who have shorter legs than grownups. Shorter legs means a shorter stride, and that means less power to get your wheels rolling; and a shorter wheel, which has a shorter roll, needs less power to get rolling. In other words, it's easier to get up to speed on a shorter wheel though the top speed is less than a taller wheel. Okay now, think back to the art wheel: shorter also means more agile. This is what some people thought, How much top speed do you need around a short track? When you also want to be juking and zigzagging across the track? That's the theory behind shorter wheels in a nutshell. Is it right? That's not the question, the question is whether it's right for you.
Width
Generally speaking, quad speed wheels are either wide or narrow. Wide is roughly 44mm, and narrow is roughly 37 mm. The general principle about width is, a wider wheel has more surface area and therefore more wheel in contact with the ground than a narrow wheel. From there, it's all trade-offs: with the wide wheel, you get more grip/power/stability but more wheel to move around so perhaps less agility. With the narrow wheel, you have less wheel to move around —i.e., more agility— but you also have less wheel on the ground, so perhaps less stability or perhaps less power. And again, what's right for you will depend on your skill and style as a skater.
Durometer (hardness)
And now, let's talk turkey about durometer. Durometer measures the hardness of the wheel; it's the number followed by the letter A. Skate wheel durometer is all measured on the A scale; there are other letter scales, but they're for other things that don't have to do with skating and therefore we don't care about. The higher the number, the harder the wheel; the lower the number, the softer the wheel. What you basically trade between the two are speed and grip/stability. A harder wheel offers more speed and less grip, a softer wheel offers less speed and more grip.
Incidentally, I try not to use "grip" interchangeably with durometer. I mean, I fail sometimes. But I try to think of durometer strictly in terms of wheel hardness or softness, and grip as how well you stick to the floor. Durometer contributes to grip, along with any number of other factors such as wheel width, wheel hub, body size, skating skill and style, and the surface being skated on.
Skating surface is probably your starting point for figuring out what durometer of wheel you need: a slippery floor needs a softer wheel, and a sticky floor needs a harder wheel. And you adjust from there: the lower you skate, the harder wheel you can get because your grip comes from your good form, newer skaters who haven't developed leg strength can get help from softer wheels, lighter bodies need softer wheels than heavier bodies, and so on.
Hub
Last but not least, your two main choices for hubs are nylon or aluminum, with hollow or hybrid hubs promising the best of both worlds.
As with plates, nylon is light and aluminum is strong. And for hubs this again means that nylon hubs flex a little bit, and aluminum hubs don't flex. And again with the trade-offs: that little flex actually gives you a little bit of grip around the turns. But also that little flex gives up a little bit of power; whereas if the hub doesn't flex, it all goes into the spin for more speed. Keep in mind that the amount of flex and how it affects your skating depends on your body weight, too.
Just by the way, aluminum hubs are really hard to get bearings in and out of. Not a performance issue, more of a mental health issue.
