If you just install a camera and video monitor, someone will have to be watching it all the time in order to catch them in the act - not very practical while you're sleeping, or at work.
If you hook the camera up to an ordinary VCR, the VCR will run out of tape every few hours (again requiring someone to either rewind or replace the tape 6 times a day). You can buy special time-lapse VCRs that will increase the length of unattended run-time, but not for cheap.
There are video capture cards that can be programmed to start recording an event as soon as motion is detected somewhere in the video image, but again, they ain't cheap.
Have you considered setting up a deer-cam? You can buy them for cheap at many sporting goods stores, they'll run for a long time on batteries, and are pretty unobtrusive.