All horses (like all people) have their quirks. There's no such thing as a perfect horse, but there is such thing as a beginner safe* horse. The key is to find a horse with quirks that you can live with. Some horses are too lazy: these are often pretty safe. The two horses I owned as a kid/teen weren't lazy, but they wouldn't buck me off.
Horse #1 wasn't really a kid-safe horse, but she liked me, so we got along well. She would not buck. No matter what. I promise, I gave her plenty of reasons to want to buck! She did run off a few times (usually with other people -- that's how she tested new riders -- once she trusted you, she wouldn't bolt), but she kept her head and had beautifully smooth gaits. Just waiting her out wasn't that bad. I was a fearless kid, and I knew she wouldn't run into anything. That mare definitely had her quirks, but I could deal with them.
Horse #2 really was a better kid horse. She was well behaved for any rider. If she got mad, she would buck, but her hooves didn't get more than an inch off the ground. They were the most pathetic bucks I've ever seen. Her quirk was that she hated crossing moving water. I'm talking about a trickle that she could have stepped over without wetting her toes. Fortunately, our trail only had the one water crossing, so it wasn't that big a problem. I could deal with her quirks, too.
All that being said, I would not deal with a horse that reared, seriously bucked, or wildly bolted. Safe* horses are out there. I'd rather find one whose biggest problem is rolling in the mud too much.
*As we all know, safe is a relative term with horses. Use common sense.