Choosing Breeding Crosses
The genetics guide will be a great help in understanding how to match your mare to prospective sires. However, if you don't want to get that in-depth, there are still some things to consider.
Perhaps the most important things in selecting a pair are making sure custom type, bloodline, stat genes, and Intelligence are good matches! You should avoid breeding horses that will be anything other than 0% or 100% custom! Without good stat genes and a decent bloodline cross, you will get a foal who has very low stats (potential) and may not race very well. Even good crosses can produce bad babies from time to time, so it's best to avoid bad crosses as much as possible. Intelligence is generally considered one of the single most important genes because if a horse is born with bad intelligence it may take them years and years to max - meaning they may not race until they are 6 or even 8.
Surfaces really don't matter, but distances do. While a horse with any distance genes will race, you will find that if you don't carefully select distances, you will end up with a lot of foals who run something around a mile. This becomes a hassle when trying to enter races, so it's best to avoid it early on. By all means, pay attention to distance genes and actually attempt to create variety among your foals. (See more info on distance/surface genes in the Genetics part)
From here, what is most important gets a little grey and can vary depending on who you talk to. Development is very important if you have horses that you want to race as two year olds, but Longevity is also important if you have horses you want to race for several years, later into life. There is no one gene that is most important, and you will have to figure out what matters most to you in your horses, based upon your own breeding goals.
Generally, a good rule of thumb if you have genotypes is to make sure a stud has a green gene for every red gene on your mare. For example, if your mare has CC cc for Conformation, you would want a stud who can fix that with a __ CC. Of course, finding a perfect match is not always possible, so you'll have to pick and choose what matters most to you even when using this method.
If you do not have genotypes, but do have genetic ratings, the same principle still applies. Anywhere your mare has low, you want to match with high (excluding distance/surface/color). Anywhere your mare has poor/fair, you want to try to match with excellent/outstanding. If you follow this method, you can end up with very nice results, even without purchasing genotypes.