I favor the TWH's. I've had a few and they are really big hearted horses. They are what I like to refer as gentle giants, although they aren't all huge or anything.
I leased a gelding for a few years that was the safest beast I'd ever met. No kick, no bite, no buck. He gaited fast and slow. He happened to be a lazy walker. They never LOOK lazy because of the way they move but they aren't nearly as firey as they look when they are moving along. Most of them gait naturally and if you are just looking for a trail horse then you don't want that high step unnatural show look anyway.
I had another gelding that lived to be 38 years old. Again, no buck, no bite, not kick. He on the other hand wasn't a beginner safe horse because he liked to go and if you didn't have good coordination he was going to go and go and go and he would pick the pace. He liked fast! He could go slow and on zero rein contact but he liked to go. Never a spook and never said no.
Black (around 38) IMG0598.jpg
I now have a mare. She's 6 with no real training. I am not a mare person but this little girl is a pure angel. She did kick a little when I got her but not out of meanness. It was out of not being handled much. If you went into her field and spooked her she popped a kick first then looked. She no longer does that, it only lasted a month until she got used to her new environment and she never made contact. She never says no and she rarely spooks. When she does, it's tiny. She is definely beginner safe for a teen or an adult and will be for a smaller child very soon. She's a lazy go and her favorite pace is slow.
With a walker you ride with your legs a little bit more forward then when you ride a non-gaited horse and they actually like a little bit preasure, they use it to shuffle. I use a walking horse bit but a very mild one although with my mare we've used french snaffles. If you want the correct head carriage though, I'd go with a gaited bit... They are cheap...
Look to spend about 1500-3500 depending on where you are. They don't actually go very cheap....