They need to be sound and durable over time. Look for consistency. Most championship teams don't win 100 percent of their games. But they win a high percentage of them. To compete for a long time, a horse must stay sound.
Soundness relies on good structural conformation.
View stallions with serious conformation faults cautiously, especially if the fault is with their feet and legs. After finding several performance-winning stallions that have stayed sound and have good conformation, review the show records of their foals. If they haven't sired foals, their performance record is still your best bet. Of those with performance-age foals, go with the stallions whose foals win consistently. After all of this, now consider pedigree.