The best advice is to arrive about an hour early for your appointment with a professional.* That way you’ll likely see the horse pretty close to its “native state.” Bring your video camera with you and use it. Watch the preparation of the horse as that is your first indication of behavioral issues. If possible, watch the horse being caught in the field if it’s a field kept horse. If it’s already up ask to see it released and re-caught after your ride.
Observe the conformation of the horse as it’s being groomed. What problems do you see, if any? Observe the tack being used. It is appropriate? If it is then you have an indication of the professional status of the seller. It’s it’s “catch as catch can” then you also have an important insight into the horse’s care.
Ask to see the horse on the longe or in the round pen. Then let the seller ride first. Then your trainer. Then you. Video the seller and trainer. Have your trainer video you.
Observe the horse’s care after the ride. Was it “rode hard and put up wet” or was properly prepared for return to stall/field? This is another indication of the quality of husbandry and that means a lot.
I’m generally agnostic on the subject of PPEs. I’ve bought with and without and suffered disappointments with and without. If you are talking high dollar horses then the thorough PPE is likely good insurance. Another factor, not usually discussed, is how you view your ownership. If you are going get deeply, emotionally involved then get the PPE even on low dollar horse because you will likely spend money on it if a problem develops. If you are going to be less emotionally connected and are willing to put a low dollar horse down that develops serious problems then the PPE is much less important.
If you can work out a “test” period then that would be a good thing. Ideally you want the test at your barn so that you can control such things as drug usage. But if you do that then you are responsible for the health, safety, and welfare of the horse. If it dies while in your custody, even if it might not be your fault, you’re still likely going to have to pay for it.
Have a reasonable sales contract if you decide to buy it. Don’t expect any guarantees. This isn’t a new car and you’re not going to get a three year, 36,000 mile warranty!!! I would not sign any contract where the seller demands rights of first refusal in the event of future sale (or anything of that sort) or wants any clause that that gives them any control over what you do in the future with the horse. That’s just creating a problem for yourself. If the seller adamant about such things then walk away.
Don’t make an offer that day. Usually it’s better to thank the seller and tell them that you will be in touch after you and your trainer discuss the matter. If you get “high pressure” (“you better act now because there’s another person coming later today and they WILL take the horse”) be polite but be firm and say “no.” Remember that “no” can be a complete sentence.
If you decide to make an offer be guided by your trainer on value. DON’T GET EMOTIONALLY INVOLVED WITH A HORSE YOU DON’T OWN!!! Don’t “rescue” it or do anything like that. Keep this a business transaction.
This is a template on how to approach the problem. Modify it as needed to fit your purposes.
Good luck in search! 
G.
P.S. I use the term “trainer” in a generic sense. It’s best that you use a professional who you pay for their time.
*Apologize profusely for having misread your calendar and just use the time to look around and see what there is to see. Remember you should keep your eyes and ears open and your mouth shut during this time.
