Everyone has an opinion, and this is your chance to explore yours. You seem to have some idea already about what you need to compliment your mare. Look at the offspring of any stallion you think you may be interested in. Look at as many of the offspring as possible. Look for similarities in those offspring. That will tell you what that stallion MAY produce. These traits may be what you are looking for, or they may be what you are NOT looking for. They may be conformation traits, or personality traits, both are able to be inherited. Stallions without offspring to view are an unknown quantity, to breed to one of those is a leap of faith, and probably not a good plan for a first time breeder. You may look for crosses in pedigrees that are similar to your mare that have worked well before, for other breeders. This is known as “nicking”, and some breeders follow these lines religiously. But other times, it makes no difference, and does not do what it has done before. That is the thing about breeding horses, nothing is ever for sure in advance, no matter what someone promises you.
Another thing to keep in mind is cost. If you decide to breed to a stallion that is far away, on a different continent, or AI only, your expenses will be greater than if you can find a live cover stallion close by that you like, and there is no guarantee that spending more money will buy you any success, either in getting the mare in foal, or in quality of offspring. IMO, a stallion that can not and/or does not live cover mares can reveal a bad disposition in that stallion, if natural cover makes him crazy and unmanageable, or he can’t learn how to politely cover his mares safely, perhaps he does not have the best disposition to sire your foal. That is my opinion, and I have always been involved with live cover stallions only. All stallions produce foals that are arranged on the “normal bell curve” of quality. That is, some percentage of poor quality individuals, a larger percentage of below average, average, and above average individuals, and a small percentage of “freaks” who are superstars. “Freaks” do not “breed true”. That is, breed a freak to a freak does not depenably get you another freak. It doesn’t matter what discipline you are talking about, but racing is the only discipline where this can be anywhere near this can be accurately measured, or is even tried to be measured. So other disciplines are far more of a crap shoot than racing is. And racing is indeed a crap shoot in this respect, even with 400 years of selective breeding previously . It is perfectly possible to breed the best race mare in the world to the best stallion in the world, and get a horse who can not win a race, this happens often. So the same goes for hunters, jumpers, any sport discipline. You must go into this plan understanding and accepting that fact. If your mare and the stallion you select both fall somewhere in the “average” or “above average” part of their respective bell curves, you can hope to produce a foal of similar quality, and a freak is always possible too, because that is where freaks come from. Also possible is a poor quality animal, who will either have to be put down as an unsound failure, or may be able to be a low level recreational horse/pleasure/trail horse. This is not known in advance, or predictable.
So you pay your money, and do the best you can with your choices, and hope for the best. Do not get sucked in by marketing or advertising, or people who make you promises in advance. Listen to what people say, but you make your own decisions.
Good luck, and enjoy the journey.