OP, if you look a bit into genetics, which is very interesting and a developing field, you will see why it’s a risky choice to breed a grade mare of mixed lineage hoping for a great performance horse.
If the mare is a mix of unknown or a mix of very different breeds, like Welsh and Standardbred, she may herself be a nice useful horse, and a good choice for a junior rider. Maybe the mix of genes has lined up well in her so that she has Standardbred height and Welsh scopyness, and good temper and nice gaits from something unknown in her background. But because she is such a mix, you don’t know what genes she will pass on. What if you get Welsh height, Standardbred pacing, and Standardbred personality? And something unknown in her that refuses to jump higher than the height of her own knees (like my otherwise wonderful mustang pony as a kid)?
A very nice stallion, if you can find one and if you can afford thousands of dollars for the breeding, is only half the equation. If people could get excellent performance horses using good stallions on any old mare, then quality broodmares wouldn’t be a thing. It is true that a good stallion bred to any old mare will in general produce a foal that is nicer than the mare. But the foal will never be as nice as the stallion.
This might not matter in some contexts. In the late 19th century, the US government sent good quality TB studs out to ranch country to help breed cavalry remount horses for the army, and good draft horses to raise the quality of horses used to farm, which would increase farm production. In these cases, the studs raised the quality of mediocre mares. At that time, horses filled the function of farm machinery, basic transport, war machine … so raising the average quality would be a huge step, especially since a lot of the farmers and ranchers didn’t have the cash to import high end horses. But today horses are mostly for sport, and we don’t need to breed thousands and thousands of TB cross cavalry horses to go get shot to death overseas. So we don’t need huge crops of good-enough horses.
Now the reason that you could send out a good quality TB or a good quality Percheron and reliably expect him to improve the mares he was bred to, was that the stallion in this case had a long and known pedigree, all of horses of very similar type and purpose. His genetic makeup from both side of his family is very similar, even inbred. But a foal only takes 50% of its genes from one parent. And you don’t always know what they will be.
There is a local barn where I live that has been breeding TB/Percheron crosses for eventing, so there are a number of these out in the local world. It is amazing the difference between them. Some look like smallish plow horses, some look like heavy TB, some look like Andalusians, and one looked like an Anglo-arab to me (she might not have been a 50/50 cross). I’ve got to assume that the heavy TB/ low budget WB horse was what they really wanted for eventing. I don’t know their entire breeding program, so no idea how often they lucked out with that. But it was a real eye opener as to the variety you can get in what’s called F1 crosses of very different breeds. What would happen if you didn’t geld one of these crosses, and bred him to another cross mare for an F2 cross? I think you could get almost anything, again. The foal might be lighter or heavier than both the parents.
Also keep in mind that statistically breeders say that even if you have two nice horses of the same breed, there’s a 50% chance the foal will be as nice as the parents, a 25% chance the foal will be better, and a 25% chance the foal will be worse than the parents (on whatever metric you choose, usually performance). If this were not true, then breeding race horses would not be so tricky.
Also if you are going to breed a foal, keep in mind that first, you don’t know what you are going to get. And you won’t really know until you start riding it at 4 or 5 years. You will need to keep this young horse somewhere for the 4 years between weaning and riding. You will need to have a trainer on board so you don’t make costly and time consuming errors in ground work and riding training. If you have a huge ranch, you can toss a young horse out on pasture and it isn’t a big additional cost (beyond vet and farrier costs). But if you are like most of us, you are going to need to pay boarding fees even to keep the young horse on a pasture (where it belongs, not growing up in a stall).
Then be realistic about the timeline. Where will you be in 5 years? if you are a tween or a young teen, as it sounds from your post, in 5 years you will either be in college or starting your first job. If you are, say, 13 now, you have about 5 years to ride this mare and have fun and make her everything she can be. Then life will get in the way. It’s fine to say now that it won’t, but it does. Where in here would you breed her, what would you ride while she is off being a momma with a foal at foot, and where will you be 5 years after that when the foal is grown up and ready to start training under saddle?
You might be in graduate school or law school, you might be backpacking in Thailand, you might have the offer of a fantastic job in your field in Australia or Alaska, and you might have either rehomed your good mare to another loving teenager or put her on permanent pasture retirement as reward for treating you so well in your teen years. It is probably highly unlikely that you are going to be right there to start sinking hundreds and thousands of dollars into training rides and lessons for yourself to make this foal your next competition horse.
If by some chance you do stay in horses and you do end up being competitive and moving up the ranks in your discipline, and you are a young trainer or working student at age 22: trust me, you are not going to want Sweet Mutt Foal as the horse to make your name with. You are going to have your choice of a wide range of purpose bred horses from your coach or clients, and project horses, etc.
IME, homebred foals very often end up not getting much training, because of time, money, lack of skills, or lack of interest when the time comes around. They tend to become pasture ornaments or problem personalities, depending on the circumstances.