I'm moving this from the disABILITIES Community Board (which is a board for general, non-Disney questions) to the disABILITIES Board (which is more for WDW related questions.
To answer your question, you want an
ECV (also called a power or electric
scooter). Those are steered with a 'yoke', sort of like steering a bike. They are pretty easy to drive with a little practice.
Electric wheelchairs are much harder to drive and take a lot of practice - the speed and direction are controlled with a joystick. You can't rent those at WDW (some of the rental places outside the parks will rent them to experienced people).
If you check out the
disABILITIES FAQs thread, you will find information about renting
ECVs and wheelchairs, including telephone numbers and links for off-site rental companies.
The best way to avoid long lines is using Fastpass. If you have an ECV, you will be able to bring it into almost all the lines, so you won't have to stand in line (you can trade the ECV for a wheelchair at the lines you can't bring it in).