As an ex Dressage rider that went to gaited, I can tell you that a well gaited horse is much easier on you than a trotting horse.
Just make sure that their gait is compatible with your back, since they move in different ways depending on breed and the way they are built. And if you have trouble at the walk, find a breed that doesn't have a huge long stride, something shorter will probably be more comfortable.
I've struggled with back pain on and off most of my adult life. Maybe I'm in a minority, but I never fell in love with gaited horses. They replace a vertical movement with a horizontal wiggling movement, which for me felt too jiggly.
For style of riding: find things you like to do at the walk, because that is the lowest impact on you and it simulates you walking. If you like to leave the arena, trail riding can be wonderfully satisfying! There are lots of walk-only rides out there, if you ask around.
My other thought is that each horse has a slightly different feel. Some horses just have really jarring gaits, while some are so smooth. I had owned a big Belgian gelding whose trot was all leg action, so his back pretty much stayed in place, kind of like prancing. I loved to ride him. My least favorite was a horrible QH-cross which moved like a jackhammer at all gaits, and even the walk wasn't so nice. I'd say to try out a bunch of horses and find one with a really smooth, consistent movement and a quieter demeanor.
And don't forget a really good fitting saddle: the right saddle can make your ride so much more comfortable. You may need to try a few before you find one that feels so comfy to sit in, but it's worth it to keep looking for the right one. Just finding a better saddle proportion and twist will help. And being sure the saddle puts you in a good position (eg. angle of pelvis) so that your back get max protection.
I have ridden a TWH and a Paso Fino and found both to be very smooth.
I have to admit though I didn't really like riding a gaited horse. I missed the challenge of the trot and it just didn't feel like riding. That being said I know if I want a life with horses I'm going to need to change in order to save my back...
We've talked about decreasing concussion when riding before so do a search and read on here. You're asking a good question but never rule out the horse you have WITH accomodations to help you. Riding 2 point makes your knees/ankles absorb shock over your back. Sitting gaits are gonna be painful. Other breeds & conformation horse types would work too. Like a long pasterned tb with long slow gaits are comfy too. Many arabs just float. Upright angles on the front end are more jarring I think. Other things like lotsa shock absorbing saddle pads, seat savers, stirrup iron pads or styles are terrific, wearing abdominal support when riding, exercises, tack so your horse doesn't pull on you, things like that are big helps!
Best of luck to you. Experiment! You can do this! Trust me! We know!!