I differentiate between how I select the actual animal and what I use for pre-selection critera (and I bet you all do too). For example, I want a certain size (like 32-34" except stallion smaller) and REGISTRY. In my case, the list of registries happens to include AMHA, AMHR and Pinto. But I would not say I select for color, because our best pinto minis are gray!
Pedigree is important to me - all but one of ours trace to Rowdy (source of a lot of pintos), plus we have Gold Melody Boy and Blue Boy (hence the grays!). Of course conformation, which I consider to be bone structure not just an archy neck. So I want relatively long, straight legs, laid back shoulder, long hip, long neck, balanced conformation (3 equal parts) and refinement, with a pretty head. I want a large horse in miniature and I don't care if it has a high or low tail set as long as the rear end has the correct conformation. If you look at our minis, I think you will see a pretty consistent type too.
Movement is absolutely critical, and I want a long stride with over-reach and stright, correct movement. I don't care about flashy or tail-flagging, but I do want ability to work off the hocks and LOVE suspension. Yes, I want good driving or dressage movement!
Temperament is also critical, as our minis need to be safe for our 4-Hers that include kids of all abilities. I would not own a stallion that did not have super temperament and pass it on to his foals.
Our three current foals are handled daily and all are fairly well halter broke already (range in age from 4-6 weeks). They all behaved well for their first hoof trim and are getting their second one tomorrow. See above for temperament.
ETA an example of what we breed for: Max, now deceased, but he proved himself in the show ring too.
