You don't say where you are located, but consider a Mangalarga Marchador.
They ride like regular horses (no special equitation techniques or equipment required). They can have three different ways of going.
First is the marcha batida, a broken trot. Not as smooth as a lateral gait, but very well suited to athletic disciplines (endurance, eventing, cattle work, etc.).
Next is the marcha picada, a broken pace (similar to a stepping pace in a Walker). Very well suited to trail riding or any discipline where there is not a lot of lateral movement required.
Finally, the marcha de centro. This is almost identical to the running walk of a 1930s era Walker. It is a good "distance gait." It allows reasonable lateral movement. It is very comfortable to ride for long periods (for both horse and rider).
A Marchador can be influenced in way of going by equipment, shoeing, or equitation practices. In this it is like every other gaited breed. But kept and ridden in a classical manner gives excellent performance without imposing a heavy burden on the horse.
Go to Welcome! | U.S. Mangalarga Marchador Association (USMMA) for more information.