I think that you need to negotiate your price first. Don’t do anything else until you negotiate a price.
Then you should find out if the seller needs a deposit to hold the horse until after the vetting. You should have a contract before any money changes hands though, and it should state clearly that the deposit will be refunded if the PPE turns up an issue that would affect the horse’s suitability for what you want to do.
Then get the vetting. During the vetting either nothing will come up that is worrisome (congratulations, you will have bought a horse!), or something will come up and you’ll have to decide whether the “something” is small enough not to worry about re-negotiating the price, or whether you still want the horse but at a lower price because of the problem, or you don’t want the horse at all because of the problem.