Jazz is a beautiful thing. Jazz drumming is incredibly fun, frustrating, and glorious all at once. It can seem easy, but is incredibly difficult.
That being said, jazz drumming will make you a better all-around player.
Don't get bummed out by the harsh comments here on the thread. People tend to go ape when someone says one thing but may actually mean another. I have a suspicion many of them don't remember what it's like to be an impulsive 8th-grader.
Anyway, here are a few thoughts from someone who is currently on the long journey of learning jazz drumming:
1) A private teacher. This is huge. And find someone who actually plays jazz. For a living. I'm fortunate to have a teacher who is, indeed, a working jazz drummer. It's true, he/she is going to assign really mundane, seemingly useless exercises, but believe me, it will come in to play somewhere down the line. I used to wonder what was going on, but as time goes by I realize everything I've been working on has been clutch to me advancing as a drummer.
2) Listen. This is true. I assume that since you want to be a jazz drummer, you actually listen to the music. So just keep at it. And it's easy now that so much is available on YouTube, etc. For me, I subscribe to SiriusXM (Real Jazz), and where I live we have a great jazz-dedicated radio station. I also make it a point to buy a couple of CDs a month as my budget allows. And listen to both old stuff, and new. Jump from some '50s bop to something modern like Trio Subtonic or The Bad Plus.
3) See it in a live situation. Find a place that is all-ages. Many local bars (where I live, anyway, allow minors in before 9 or 10 p.m.). It doesn't need to be some swank high-priced show, it can be a local trio in a bar or restaurant somewhere. Seeing how people work with each other (Like they say, jazz is a conversation) in a live situation is a big part of learning.
4) Books. I got both Riley's book and Chapin's book. My teacher suggested I shelve Riley for now, and concentrate on Chapin. It lays a better foundation, and then I can move on to Riley after I get a grip on what's going on in Chapin.
5) Brushes. Get started now. Brush work is a life-long pursuit in getting good. Everyone does it differently. But pick up basic ideas, and work in what you hear, and what you want to hear. And play it. All. The. Time. And then another half hour.
6) Drum Kit. This is where people on this board (for the most part) are right. It really doesn't matter what you're using. Any kit is a jazz kit. Look at 2015 DeJohnette versus some dude from '59. Completely different kit, but still playing the same stuff (sorta). It really comes down to technique, what you want to get of it. And price doesn't matter. No. Really. It's true. You can find something for 450 bucks and make it epic. Plop money down for cymbals. That's where the money should go. And it's fun. The never-ending hunt for some holy grail of some guy selling an epic cymbal for dirt cheap ("I dunno, it was sitting in the attic and I just want to get rid of it) -- I scour Craigslist daily looking for some nugget (I got an absolutely virginal Blackrolite (not a cymbal, but you get where I'm coming from) a few months back for 85 bucks).
Good luck on your journey!