The most common form of hand control is the Push/Pull lever, normally operated by the right hand you push to brake and pull to accelerate, which operates the foot pedals mechanically; this normally has an integral indicator switch mounted on the handle and is usually used with a left hand operated steering ball.
A floor mounted push/pull lever is an alternative type that is operated by the left hand and used with a right hand operated steering ball. some people find the position of this to be more comfortable.
The Electric trigger throttle and brake lever has a lighter to operate electronically operated accelerator and a mechanical brake lever. Again usually used with an integral indicator switch and left hand operated steering ball.
The radial accelerator/push brake hand control can be easier to operate for people with poor finger grip, you push down towards the floor to accelerate and push away to brake. again used with a right hand operated steering ball.
Ring accelerators have the advantage that you would steer conventionally with two hands on the wheel, the accelerator ring can then be operated with either hand whilst simultaneously controlling the steering. The accelerator ring could be mounted over or under the steering wheel (an over ring or under ring accelerator) and is used with a right hand operated brake lever.