Steering wheel with optical or multiturn
I would recommend trying one of these 360 degreee continuous angle sensors. Current technologies for angle sensing revolve around optical, resistive and hall effect properties as you identified. Generally, the highest end products use hall effect as it is completely analog and non-contacting. Building a sensor from scratch can be very difficult to optimize so I would recommend one of the packaged solutions and feed that to a microcontroller of your choice.