I would go for as simple as possible - 1k resistors between each contact. Then its easy to convert the ADC input to a switch-position number, and this in turn can be converted to any function you want, linear or otherwise. For a 12 position switch that comes to 11k in total which is less than 0.5mA per switch which isn't too wasteful.
One issue is that as the switch moves the wiper might be floating briefly (or simultaneously connected to two neighbouring contacts). The code will have to identify and reject such 'bad' values. Reduce the 'floating input' problem by a capacitor of 0.1uF or so between the wiper and ground.