Exactly what OTM said!. Find a stallion you like (and leading sire results on USEF are a great place to start), and then look for breeders using him. You might even prefer to lease a mare (many larger breeding operations offer this) and have her bred to the stallion of your choice. Obviously, this is a longer-term plan, but then you’d really get exactly the lines you want.
However, the risk with breeding or buying in-utero are not insignificant. There can be all sorts of health issues with the foal, and even if it pops out healthy and gorgeous, it may end up being too big/small/hot/wrong gender/etc from what you were hoping for.
And someone on COTH has a signature line something like: definition of HORSE: A 4-legged mammal that spends its whole life trying to find expensive ways to die.
I once purchased a lovely colt at 1-week old. He had the bloodlines I wanted, and was gorgeous and personable. He did some limited showing on the line with success and was lightly backed as a 3yo. That summer he developed suddenly increasing ataxia, and subsequent vetting showed he was a severe wobbler. He was put down that fall. There are thousands of stories of heartbreak to balance the thousands of happy endings.
If you can afford something ~2yo-ish, you’ll have a better idea of size, type, temperament. To find something affordable and still available, you might have to do some detective work and find a smaller breeder, or take a chance on newer bloodlines, e.g. the sire and dam the offspring of the bloodlines you’re looking for, vs direct son/daughter.