I don't think there is a "best" We have 3 registered TWH mares. 1 is built like a tank and is ridden in a Circle Y custom saddle that is extra wide. My mare is narrow with a broad flat back - I ride in a Tucker River Plantation saddle and also have a The National Bridle Shop western saddle. My daughters TWH is fairly narrow with a deep barrel and she rides her in a wide width Collegiate dressage saddle.
All of these horse have been ridden in other saddles and did well. They all gait really well -we just make sure there is enough should clearance
I'm a personal fan of Tucker saddles and hear they make some nice gaited saddles as does Circle Y.
They're really helpful with fitting as well and the saddles can be customized if you collaborate with a dealer.
I have two TWH. I use a Fabtron Synthetic with gaited tree for both. I bought the first one 6 years ago for my mare, with the intention using it until I found a "real" (leather) saddle. I'm happy with it and I've stopped looking for anything else.
When I bought my gelding, I found that he goes well in the same saddle. So that's what I bought for him also. Reasonable price, works well for my horses, and lightweight.
I ride Rockies and TWH. Love my trooper saddle. I think it’s the most comfortable saddle I’ve ever ridden in and it fits all of my horses so far ( I have a yearling and 2 year old so not sure about them yet.)