I've been doing the self same thing for two or three years. I've spent years collecting nostalgic TV. Three years ago I bought a Phillips DVD recorder from ASDA. Just link a Scart lead from the DVD to the Video player/recorder and off you go.
The editing facilities are a bit crude, but you do get the hang of stopping and pausing the video in the right places (adverts and stuff). Once it's on DVD, you can work wonders on a computer with the right software and a bit of determination.
If you're copying commercially made videos, you might have a problem with electronic protection.
Hope this helps.