I've had the same issue. And like others have said, buying a DV camera just for that seems a bit expensive since you'd need to also by a card to connect the cam to your PC if you don't have one. I agree with gmask -- you usually can't go wrong with a pinnacle card. You can get an analog capture card from them for $150 or less with software to allow you to export your movies. You can hook your VCR right up to that. Make sure you don't just get a TV-out card cause you'd prolly havta play it full screen and if you're resolution isn't high enough, you'd lose major quality.
Make sure you got a fast enough hard drive, too. Won't export if your HD can't keep up.
Good luck,
-c
P.S. You said the files won't fit once they're loaded in? What did you mean by that? Cause if you can't fit them on your pc, none of the solutions would really work anyway.