Welcome to the wonderful world of horses :)
When you first start riding you'll essentially be picking between two 'styles' then, once you develop the core understanding you'll be able to follow through in that style into a more precise discipline.
There's English and Western. For the core basics of riding the differences are your seat, in traditional western they have more of a chair seat (sitting more on your back pockets with your legs a little more out in front of you), you neck rein to steer, you typically do not post the trot (though it can be a good skill to learn and many modern Western riders do post for comfort's sake). English riding you typically have a more balanced or forward seat, sitting with shoulder, hip, heel all in line. You'll steer using direct reining (pulling left or right to turn) and you'll typically post the trot.
Once you've learned the basics of whichever style you're most interested in you can develop those skills into a more precise discipline.
-numerous cattle working sports
There's a whole bunch more in both of those styles but I don't think I could go into them all :P You could try taking the basics in both styles and deciding which fits you more.
Good luck! Have fun!