All you need hardwarewise is a capture card which costs about 40-80$ USD depending on technical specifications.
I'm not very familiar with computer stores in USA so I just used Pricewatch to find cheap retailers. On today's capture card you can find at least 3 different capture chips (I'm only going to mention two).
One of the oldest is BT878 which still provides good quality and has great software support. Another one is CX2388X which provides better picture (yes, it's noticeable) but is more sensitive to noise and software support isn't great but it keeps getting better.
A BT878 based capture card is Pinnacle PCTV Pro and it costs about $80 USD.
A CX2388X(3 I think) is PixelView PlayTV Pro Ultra which is a bit cheaper than the Pinnacle card, 56$ USD.
I personally own a PixelView PlayTV HD, it doesn't perform as great as Pro Ultra but I think it's a great card considering that you're using an analogue source (antenna/vcr) and it doesn't cost that much either.
As for DVD-Burner I suggest that you get a NEC ND-2500A which is also reviewed on this site.
For more information use the search box.
I guess t:is is very personal but I've used this setup without any issues.
Postprocessing: avisynth , VirtualDubMod
Encoding: TMPGEnc Plus
Authoring: TMPGEnc DVD Author
Some may say this is unnecessary on dvds but I strongly recommend that you teach yourself how to use avisynth to reduce noise and improve the image. It may take some time to get it good but you're only going to capture it once anyways. If you want to know more I suggest that you visit Doom9's forums.
You'll need about 20gb per hour if you want to capture at full dvd res without any lossy compression (recommended).
I guess that's all you need to know for now.