Warmbloods (of most varieties) are purposely bred for performance is dressage and showjumping. They generally have the height, conformation and breeding to have the best chance to excel in these disciplines.
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.