Having had horses my whole life, here are my suggestions. Find perhaps a local 4H teacher or some other known expert in horses and take lessons from them. If you don't have a local 4H teacher (ours here used to teach private lessons to all who asked) see if there is a barn nearby with a good solid teacher. As far as what to ask an owner when considering buying their horse: see if you can get your instructor or some other person very knowledgeable in horses to come with you and meet the horse in person. Although it's really great that the horse you're considering looks "sweet" in photos, please realize that the owner quite naturally has a very real desire for you to buy the horse, even if it's the totally wrong horse for you. Another person with you might be able to ask some really hard questions such as, is the horse up to date on shots and worming and hoof care? Has the horse been professionally trained? What exactly has the horse been trained to do? How well does it lead? How easy is it to catch? Can they demonstrate that for you? Has the horse ever been lame, or sick? And so on....
I remember once going to see a horse, and to my complete surprise, the owner took us IN HER HOUSE, and showed the horse to me in the back yard through the window. She said that I could "see" how "gentle" the horse was. Well, it turned out the horse was plum wild and would run like crazy if a person got anywhere near her. I did not want a horse to look at out my window, LOL... Plus, how do you haul a horse to your house if you can't even get near it? Sometimes, the person is so motivated to sell, they will tell you about anything. You do have to be careful. There is a reason that we have sayings in our language like "buyer beware" and "horse trader".
Generally speaking, I advise a beginner to get a horse that is much older than 5. Don't get me wrong, there are 5-year-olds out there that are great, but just generally, a horse that is 15 is going to be a steadier mount, far more reliable, easier to handle, and will have gone through all the "silly" stages of life and have settled down. People tend to over-horse themselves, because they see a beautiful young horse and really want it. Then they end up with a horse they are scared of, and what fun is that? Yeah, sure, that horse might look really impressive and beautiful, but it's more important to be able to actually *handle* and *ride* your horse, unless you want to be like that one lady and just look at your horse out the window...