If I purchase a Tivo or DirectTV DVR, can I record images from a surveillance camera?

I do not have (nor do I plan to obtain) a subscription to Tivo, DirectTV or any other cable or satellite service. However, I was wondering if I could still purchase a DVR for the purpose of recording surveillance images at my home. I can record images to VCR but the strict limitation on the number of hours that can be recorded is inconvenient. Any other neat tips would be great too. Like, can I also connect a motion detector to the camera (which is wireless, by the way) so that it's not running when there is no activity in the area?