Find a trainer or instructor that you think you'd want to work with. Introduce yourself, have a lesson on their horse so they see how you ride. And make sure they're on board to help you find a horse.
First ask a lot of questions. Then go out there and make sure you see the horse be caught, saddled and then ask the owner to ride before you. If they lunge first that's a bit of warning sign. Take note of what bit they use and ask them to walk, trot and canter the horse each way. If possible, as to see it ridden outside of an arena.
Then you or your husband have your ride. Put it through it's paces. Handle it on the ground, see if it's respectful. Then go away and show your trainer a video of you riding it, or something, and get their advice, and then bring them out. Get them to try the horse out, put it through it's paces.
Ask for a trial, it's not really a red flag if they say no, but it's preferable. Then decide if you want it, and if so buy it.
Try and find horses through people you know, ask at the local riding clubs and there might be a been there done that horse for sale.
Also, I don't know what your budget is but keep in mind that good horses don't often come cheap. A real quiet, reliable horse can go for a fair bit.
Age wise, I'd go over 9 but under 16, give or take.