Don't use the stable's vet. It puts the vet in an awkward position. Pay the vet yourself. They are working for you, after all. I disagree here.
Every trainer has horses for sale, and they get bad ones as well as good ones.
I would suggest using a trainer that has been recommended by other horse people in the community to help me find a horse, but NOT one of their own horses. By all means, pay them for their time, and pay them well. The cost of a horse varies from area to area. The initial buying of the horse is the least expensive part. Few first-time owners should give horses shots.