Breeds do tend to have certain characteristics, but not every individual in a breed will have them. Different breeds seem to suit different personality types - I once did a hilarious exercise where I got people to do an online colour personality test and then matched them to their best breeds by the number of reds, greens, blues etc they scored. It was all rather tongue in cheek, but it was quite astonishing how many people said, "Yes, actually, I do feel more affinity with that breed".
The reason breeds are different, especially those close to an ancestral type, arabians, fjord, shetland, iberians etc, is that different conformations and different temperaments were a better survival strategy in the ancestral environment.
Running fast is not much use if you are stuck in a bog, but kicking hard and bucking are all good in that situation. The famous pony trait of dropping one shoulder is a great defence if you are dodging around in a forest edge. Attack horses, these are the cow horse, Iberians, 1/4 horses, many gaited breeds, are ancestral mountain horses, where running away is only sometimes an option. Interestingly, plains dwelling Prewalski horses behave more like cattle when under threat, forming a tight group with the adults facing outwards.
There are quite few people who link the horses physiology, conformation, to their personality. There is a fair degree of truth in this, but most of the explanations I have seen range from the faintly mystical to the downright batty. With the exception of breeds that have been artificially selected for "desirable" traits that are not actually very desirable from a survival point of view (e.g. seahorse heads in arabians), the physiology of horse will reflect its ancestral environment, and thus dictate the inbred survival strategies that we think of as personality traits.
So the big thing is to know yourself, and choose the type of horse most likely to chime with you. Any fit and well horse or pony, especially in the height range you are specifying, will be able to do all the things you want. But only a horse that matches or compliments your personality will try for you, would probably die for you!
As a rule of thumb, cold bloods need positive, encouraging people. If they get scared, they will use their weight and strength to defend themselves. Hot bloods need an agile mind, as they will run when scared, but they don't mind neurotics, they are quite happy to be neurotic beside you. Warmbloods need calm people with agile minds - they can be unpredictable as they display both personality types of the original crosses, hot and cold. Iberians and arabians, although from quite different ancestral backgrounds, need people who have a sense of the absurd. Ponies are a law unto themselves, but are often much quicker and more agile than people expect.
There is no best breed, but there is often a best breed for an individual.