As the scale differences were noted above, I'll make note of a few tangible differences.
The scale you choose depends on your wants. If you are looking just to have some cars fling around the track, with less car realism, HO is the way to go. 1:32 scale offers much more car (details!) and "driving" realism, but "less" track will fit in the same space. 1:24 is mainly (save select carrera components & the ninco karts!) the plastic wings that throttle around a routed track at your local slot track. Low realism, high speed. This is rarely done in home.
Most of this forum's users are 1:32 people, with a sprinkling of HO for added flavor.
We race 1:32 scale on plastic and routed wooden tracks, at home, a club, or both. manufacturers in this group include Scalextric, Ninco, Carrera, Artin (all four make track AND cars, more on that later), Fly, Slot-It, and more. Cars come in all varieties and can be run out of the box, or tuned for increased performance. Most of this forum will tune cars, trying to get the most out of each car, while there are still plenty who have fun with the cars as they are sold. There is no wrong way to go on this, as you can get as far into this hobby as you want and are comfortable with. This forum is always happy to help, no matter which way you go.
As for buying your track, you again have many options. Scalextric, based in England, make a great track (Sport System) which is smooth but offers good traction. Ninco, based in Spain, makes a wider track that is a little rougher, thereby offering a little more traction, though some believe it can wear tires faster. Carrera, based in Germany, also has a wider track that runs relatively smooth, but it has a striped line between the slots to simulate a road. Artin is an older track system, a favorite of many old timers here is similar to Carrera in having a stripe, and has a easy fit connection system. There is no wrong way to go and there are many websites (most of which linked from the links section of this website) that offer more in depth comparisons. Be warned that they, like my very own post, can be biased, so read as many as you can to gain a better overall perspective.
If you live in the US, Scalextric and Carrera are generally the easiest to get ahold of, and expand with more track, but Ninco is found on many shelves as well. Shop around and you'll find great prices, and great service. (We love Judy at Fantasy World!)
Always feel free to post questions.