Tom
Sound like a nice project.
I would do it as follows: Connect the kinect to your pc (Microsoft has the kinect API) make the pc do all the thinking and calculation. The PC sends messages to the arduino over the serial connection on how hard the motor needs to run (that is change the speed of the motor)
On how to read the kinect you will have to go to the kinect forums. There is probably more help there for that part.
On the motor: You will have to decide on what you want the motor to do. On average a "standard" motorshield will drive up to 2 Amps DC on 24 volt DC but there are shields which can handle more than 30 Amps DC. An external dedicated driver can handle much more. So it is more a matter of how much money you have and how big the engine needs to be.What does the engine need to do?
If you want to go for AC there are other considerations.
From a code point of view: On driving the engine see the motorparty example.
I hope this helps you out a bit.
Best regards
Jantje