Other people have chimed in with more experience about what the OP should look for in a prospect, but I have to throw in regarding the price that it’s possible that the owner isn’t itching to sell this horse at all–all horses are for sale, but that doesn’t mean that the owner is very actively trying to sell the horse, if you know what I mean. This could be a “I don’t really need to sell this horse right now, but it would be nice if I could get…”
OP, I don’t need to tell you this, but it’s worth remembering that the horse world contains people for whom spending $250k on a horse–that could go lame tomorrow and who will possibly depreciate in value if the training and showing doesn’t go as planned–is a drop in the bucket. The fact that you don’t feel this way–God knows, to me, $250K is money I would claw onto and throw in an index fund, to be honest–indicates it is too much for you to part with. This isn’t something that’s shameful, rather it’s a reality check. Add up the initial cost, training, board, possible vet and farrier bills, showing costs and take a good hard look at that figure, and calculate the opportunity costs of what you’re sacrificing. Might a less costly path in the sport give you equal joy (and it doesn’t have to be bringing up a “baby”)?