There are so many different aspects to look at, and sometimes a pony you think is going to do brilliantly just doesn`t and one you think has no hope goes on to amaze you. There are a few things I would take into consideration when deciding on a pony:
Some people will start off by telling you all about the correct style and conformation of the ideal showjumper, but in reality, there have been so many horses and ponies that if you looked at them you would never say they could jump, but their hearts and attitude have made up for it and they love what they do so much that it carries them through to the top levels. Having a correct conformation and style helps a lot, and is very important, but it will only bring you so far - attitude will do the rest.
You need a pony with spunk - one that is brave and level headed and can focus on the task at hand. When you go to look at a youngster or a novice pony, put up a simple, solid jump and free lunge him over it. What does he do? If his ears are pricked forward, he looks eager and he is not scared to try the jump, then you already know you may have a good pony. Only put him over twice. It is also a good chance for you to check his technique from the ground - a good pony will lift his legs well and might even bascule nicely over his fence. (Bascule = the round shape he makes with his body when going over the jump) That will tell you plenty. Getting to the top is tough and it takes a lot of work and the ponies are under a lot of pressure. You need a pony that can handle the pressure put on him without going sour or losing his sparkle. In fact, many of the top horses and ponies are rather disagreeable in their stables, but that is because of the pressure that is put on them to perform. The pony should be level headed though and be sensible at all times.
When you ride the pony, he should be willing and pay attention to you - even if he does not have much training, or is young and unbalanced, a good pony will always be keen to offer you something when you ask it. He will give back.
Be careful of the pony that is TOO careful when he jumps - they are the type of pony that look great when things are going well, but they quickly lose their nerve when things go wrong. A good pony will always listen to his rider, but when the rider falls short; he will step up and help out without fear. The kind of pony to get you out of a scramble, as it were.
2. Style and Conformation
You are looking for a pony with good conformation - avoid things like long, weak backs, upside-down (ewe) necks and goose rumps, as those are weak. Look for short, strong cannon bones and clean legs.
There are some ponies out there that really do just have poor technique and you are not going to be able to change it much. There are exercises and grids that will improve technique, but really try to avoid the pony that crashes through his jumps, stops, twists or dangles his front or hind legs. Look for clean, crisp jumps, with the legs lifted, a nice round back and a keen expression.
Choosing a pony to compete on can be very tricky, and really it is a bit of a gamble unless you are buying one that has already proven itself in the showring. If you are looking, I would suggest that you take an expert with - someone who actually competes at a high level - and that any pony you decide on has a full vet check before you make any final decision.