yes, as was mentioned, you do not want speed but rather style and manners. A horse that moves smoothly and maintains a single gait will place better than one that rushes.
Practice running with your horse and teach them to read your body language as far as changing direction (smoothness of turns and direction changes).
Also practice many types of jumps and focus on the manners and a quiet way of going.
I know we just started in Hunter this year, but our big one has been "getting over" himself in the ring b/c he's been a halter horse, he thinks it's time to be spunky in the ring so I MAY change to Jumper as my gelding matures since I didn't want to push him too hard his first year jumping (he's just 3), but rather focus on learning and conditioning up. Just offering some things I've observed.
One of the top Hunters in our region is a trotter. He trots fairly quickly, but he keeps the same exact pace and clears each fence neatly, with exactly the right room to spare (i.e. not overjumping or underjumping the fences), and he moves smoothly off his handler as in when she moves her lead hand over, he begins to turn/bend. It's great to watch, and obviously has taken them a long time to get perfect, but it's the epitome of what the rule book describes.
Liz M.