I got into horses at 50. If I had to do it over again, I'd hire a good trainer, have her watch me ride, then give her a budget and pay her to find a good horse. And that is tougher than it sounds, since A) a horse can be very different around one environment, or be like my mare, who is a sweetheart 9 times out of 10, but on that 10th time , and B) sellers lie. Not all sellers, but a lot.
Sometimes it isn't the seller's fault, in the sense that a horse might be great with an experienced rider and behave beautifully, but will take advantage of a new rider.
To make matters worse, you have horses like my gelding. With someone who has ridden a year or so, he's great. With a brand new rider AND me standing near watching, he keeps an ear on me and behaves according to my expectations. With a new rider and no one around, he administers a riding test - not violent, but he'll disobey and see if the new rider corrects him. If not, he'll then do what he wants.
So if I rode a horse in front of its owner, I NOW would check to see if it is paying attention to its owner. If he keeps an ear on the owner, then I'm probably not seeing the real horse.
Like most who take up riding and buy a horse as an adult, I didn't appreciate the complexities of a horse's personality - or owner's! Looking back, when someone is selling a horse that was used for endurance racing, then left unridden for a year, certain phrases jump out as warning signs: "racing" and "unridden".
And while it is possible to get a good horse who was "donated to charity", I'd add that to the list of things a beginner shouldn't want to hear. 3 of the 4 horses I've owned were donated to raise money for a charity, and 2 of those 3 have, WITH PROFESSIONAL TRAINING, turned into very good horses. Just remember to add $2000 in training to the asking price!
And the third? She's in my backyard now. The trainer we've worked with will be here in 30 minutes for a session of training me to train her. I still have soreness in my hip from a bolt/tumble 2.5 years ago. And I adore her. She is the horse that made me want to ride, and has forced me to take lessons, read books, pick people's brains, hire a trainer...she was one of the worst possible horses a beginner could buy. She is 10 now, and at our current rate...well, if I'm not killed or crippled, then we ought to have things worked out by the time she is 15.
And yet, when I was buying her, she behaved fine for my youngest daughter - who now refuses to ride her for any reason!
Like I said, if I had to do it over again, I'd hire a good trainer, have her watch me ride, then give her a budget and pay her to find a good horse. And then hope she was honest, and a little bit lucky.