Set up your appt, show up a half hour early. You allowed time for traffic and didn't need it
If I'm looking I just ask people if sometime on insert day would be okay because my schedule is hectic and I will get there no earlier than a and no later than b.
If they are tacked upon arrival, un tack. Check the horse thoroughly without tack and how it behaves in hand. Under saddle is only a small part of the grand scheme of things.
Look for signs of sedation, sweating, glossy or droopy eyes, pupil dilation, relaxed/possible drooling mouth, slow to move, etc. Ask to watch the horse lunged first, watch the cadence of it's gaits. If it isn't rhythmical that can be an indicator. Some also get excessively gassy or have loose stools. Also listen to it's breathing while resting. Some may grunt or roar while working but at rest it's a red flag.
Ask lots of questions. Ask for references. Ask for past owner information and follow up on it. I sold a broodmare of my gpa's a couple years ago and had a call a few weeks ago. They wanted to know about the mare's performance record as the seller told them she had an extensive show career as a youth horse. She did not. She was just a well bred mare with good confo that he raised a few babies out of. She was broke to ride but not a show mare and certainly not a youth mount.
Depending on price tag, get a PPE. I'm confident enough to look myself without one but if it's a good amount of cash being spent I take my vet with me.
Don't buy the first visit. (unless you are certain it's the right one and honest seller) Let them know you are interested (if you are) but you have looked at others and need to make a decision and will get back to them in x amount of time. In that time between do a surprise visit.