Steeplechase horses are all Thoroughbred horses. Steeplechase trainers search the flat tracks for horses that will make jumpers. They usually decide to buy when the combination of pedigree, race record, conformation, and price come together. Geldings who aren't making big money on the flat tend to switch careers and become steeplechasers. Sires like Northern Baby, Alleged, Kris S. attract their attention.
Northern Baby is the premier jumping sire.
He's sired several champions and tons of stakeswinners. But back to the schooling of these horses. Generally this is how it works. The horse will be introduced to jumping slowly and deliberately. They start over rails on the ground or small logs and always with a lead horse.