Connemara s are super they maybe quite small but boy do they jump !
The breed isn't as important it's more the individual horse, as Caoimhe says. Especially in the lower levels. I've seen Connemara ponies jump 1m50. However, Warmblood's in general do dominate the showjumping world. It takes a really special horse to get up to the Grand Prix levels though. But at 1m 60 just 60-100k warmblood isn't going to cut it. Most Grand Prix jumpers are multi-millions of dollars in the 700k-15 million range. But a paint or quarter horse is relatively cheap; most sell for a couple thousand and they can still jump up to 3ft and take u up the lower levels and have a great temperament. warmbloods and thoroughbreds tend to be a little spookier and hotheaded but some also can be really chill. Off the track thoroughbreds are also a good relatively cheap option and dominate the eventing world currently. Still can be used for jumping though. Just consider your options and make sure you have chemistry with the horse. It can be an amazing 4 million Grand Prix showjumper, but it doesn't work out for you and does fantastic with another rider. It's not just about the horse, it's also about the horse and rider combination. Don't get so hung up on the breed and really look at the horse as an individual. Good luck and happy horse hunting!
It really depends on the horse. I flat school a 148cm pony, who is jumping 120 with his owner and his breeding is unknown. You could buy a well bred warmblood or Irish Sport Horse with potential to jump 160, but if you over horse yourself, you won't be successful jumping 60 on it. You could buy a horse of unknown breeding, and it be the perfect horse to bring you up through the levels. The breed is considerably less important than the horse itself and how much it suits you.