Although most horses have the potential to do well in at least low level jumping. You don't need a perfect jumper. If you decide to focus on jumping your first jumper isn't going to be the one to take you all the way.
I believe most horses can successfully jump course of 1m - possibly bigger. I've seen stock horses jump, quarter horses jump, ponies jump, TBs jump, Arabians jump etc. I'd look for a horse that is reliable, athletic and with a good temperament. I wouldn't recommend a pure arabian, they are not built for jumping but a nice cross breed would do nice. I have seen Anglo Arabs, QH/TB and draft horse/TB crosses all be successful in jumping.
I personally think Warmbloods aren't great beginner horses. They are generally big, strong and discipline specific. Its just my experience though. For English I'd look at maybe a cross breed of some variety, perhaps half TB? Half TB with almost anything seems to turn out reasonably well.