The limit of an A/D converter sample rate may distort the video signal. If you can live with a little distortion this will work fine. You will need to define that "exactly" means to you.
Speed will also need to be defined.
A unit like "TiVo" may work for you. It has hardware video compression in the box.
There are PCI video input cards available for PCs.
How big a unit are you trying to build ?
Its called a video tape recorder.
Good luck, you have only scratched the surface in design and cost.