Hi and welcome to the forums. I just recently did this myself, and thanks to a friend who is very into this, I learned of the following procedure(s) to make an optimal copy.
Best way to do it, for least quality loss, is to output the VCR into a Digital cam DV Recorder. Then (as most DV cams have, the one I used was a sony) you use firewire to send the the DV tape into the PC, we use Adobe Premiere Pro 1.5, after which we used TMPGEnc Plus to encode to mpeg2. Remember it is all done in real time, so you wait while basically playing the movie, get dinner or something during this. Just remember to dry run the DV tapes one time to set a proper time code on them, you will see this is important when incorporating with software into PC, just run a copy of a tape in blank, thats all. Then you need a burner and any burning software like Nero, and you are all set. Make sure you got lots of HDD space, and keep in mind that each DV tape holds only 60min, my 2hr home video took up 26GB as it was in RAW AVI form, before the encoding process, and I used 2 DV tapes for it.
BTW, get MainConcept DV codec for encoding because MS DV encoder is way outdated and crap.
If you do not have access to this equipment , the next best quality achievemnet will be with an RCA DRC8300N although it is pricey, its 1 click of a button and you do nothing else, kinda self explainatory if you read about its specs on any site.
Given your current hardware and PC setup I suppose will give you the 3rd best output, and you will need to see if the Radeon card has a capture in (usually S-Video) port, if not you will need a capture board, might need to buy one, otherwise the procedure is the same as in the first solution with the software bundles and the encoding process, minus the DV tapes step.
So those are the 3 flavors of options you have for quality achievments possible.