One thing to keep in mind is to have a reasonable budget. A BTDT safe, beginner/kid's horse with good training on them is not going to go for $500. I see ISO ads everyday where someone is looking for a beginner/kid safe mount, show record preferred, between 10 & 12 years old, some color and patterns, not more than $500. I have a couple of horses that would fill the bill for safe, sound, sane and good basics, one has been through a police horse desensitization program. Both are good mothers and easy to get in foal (if a person is looking for that) and I ride both on a regular basis. I would THINK of selling them between $3500 (that one has a scar on her leg, cosmetic only) and $5000 for the other, but ONLY if I liked the person who was interested and decided they'd give an excellent home. One is Shining Spark bred and the other is cutting bred (Listolena is her sire) but too lazy to chase a cow. They're both excellent horses but I wouldn't even consider selling them for $1000 or less.
So you need to have a clear pic of what you want, how much you can spend, be sure to have a PPE done whatever you choose. Just heard another horror story, gal bought a reiner mare, in foal, for $5500, gorgeous animal. Asked how she rode and she didn't have the owner ride her (and owner didn't offer, BIG red flag) and she didn't try her out before buying and no PPE. Got her home to ride and she got tossed, drilled into the dirt more like, got up and got on again and got drilled again and ended up in the hospital with a TBI/concussion. Obviously, they saw her coming. Owner or trainer absolutely HAS to ride the horse before you get on it. If they won't or say they can't, then they should have a sub to ride for them.