Learn to jump on a horse that's jumped a lot before.
No, seriously, this is THE single best piece of advice anyone can give you. If the horse knows what it's doing, and its first experience of jumping isn't with a green rider (green to jumping, I mean), it will be far less likely to present you with problems while you're still learning the basics. If you're new to jumping, you WILL yank on your horse's mouth sometimes, and it takes a very special horse to keep trying anyway, or a horse that knows that jumping doesn't always mean "ouch, my mouth!" and can put up with the pain knowing that it will gradually go away.
Always remember, green+green=black+blue. My first experience of jumping was on a very steady old plodder, and then, years later thinking I knew what I was doing (even though the highest I had ever jumped was 2'), I bought a young horse to train up. NOT smart. I totally wrecked him. I later got a pony that was also green to jumping, but that pony was a lot more tolerant, and I was a lot more confident with him, so he learned along with me. Not the ideal situation and I still have bad habits from it but it worked ok.
Then I got my schoolmaster, and he showed me just how much I didn't know. He started out going awesomely, and then started rushing and bolting at fences. I lost a ton of confidence because, in my self-righteous insistence that I knew what I was doing, I didn't have a coach. I got one, and slowly my confidence increased again. Now, I hit the right spot 8 times out of 10, I can usually see 3-4 strides out if I'm going to be in the right spot or not, and we're jumping up to 3'6".
Long story short I have around 7 years of consistent riding & jumping experience, and I still had no clue what I was doing up until roughly a year ago, because I'd only ever been on slow old plodders or totally green jumpers, and then with all the issues I've had with my boy I didn't really learn for quite a long time.
So, learn to jump on a schoolmaster with a REALLY good instructor, and you'll learn at your best possible pace. Learn on a greenie, or even on a schoolmaster with no coach, and you'll learn a lot more slowly.
You may struggle with the transition, by the way, because English riders typically ride with shorter stirrups (dressage excepted), and in MUCH more open saddles. But it's heaps of fun and will be worth it!
A CLEAN SLATE FOR THE FUTURE