For this kind of projects, you don't want to share the ground - you will never know what you may pick up from the ground.
So you should think about isolation.
Digital signals can be easily isolated via optocoupler. Analog signals are tougher. If you, however, use a V-F converter, that can be done fairly easily and it is simple for the arduino to count frequency, or you can use a F-V converter to get back the analog signal.
It also provides the option to isolate via signal transformers.