I have 5 criterias, but the perfect horse doesn't exist. For an eventing horse, the first thing I look is blood, the origins, because that's the only things we can't work on. I look at the quality of the jump which is more and more important. Locomotion, if he looks good for dressage. I also look at health, because this sport requires rigour, it's hard to start with a health handicap.
Feeling also has a great role, if I look at Funambule for example, he only answers to 2 criterias I think, but it's the cohesion between us that does everything.