Ideal projection solution for Kinect hack performance
As AJ Henderson mentioned, you program the Kinect with a PC using various software packages, either ones that support Kinect natively, or by using the Kinect SDK. One that we use often is Derivative TouchDesigner. There is a free educational version you can download and use for non-commercial work.

Projector wise, I'd recommend something of at least 10,000 lumens. Depends where you set up the projector, and how much throw you need. You can use this handy calculator to help you get closer to what you need. 

http://www.projectorcentral.com/projection-calculator-pro.cfm