Ive done this with a tape before. Luckily I had a tv tuner with an s-video in. Once you get the video to your pc in whatever format (probably mpeg), the best would be to re-encode the video with virtualdub to allow you to have a play with the filters and see if you can clean it up a bit. Also load the audio into audacity, and you should be able to make it sound MUCH better.
You can pick up a suitable tuner for ~£25-£30 from ebuyer, then when youve recorded your tape, you can use it to watch tv too