first of all I would say go with a capture card not a USB capture device (ie. dazzle usb capture devices). An all in wonder radeon would be great... look for a cheap old one like a AIW 7500 or lower if they wont be doing any gaming, the AIW radeon 9700 has some cool features that will "clean up" the videos to make the image quality better but it definetly comes at a premium. The AIW cards come with Ulead video studio so they can also edit their videos (add titles, wipe effects ect.). You can also use a PCI capture card such as the TV wonder PCI (again dont get the USB one).
Make sure whatever capture card you get has "composite" inputs (AKA RCA inputs... those yellow, red and white inputs/outputs that are on VCRs/TVs ect). That way you can just connect the VCR to the Computer just like you connect the VCR to the TV, that will also take care of the audio.
Find out their price range and see if you can get a DVD burner and take the cost of the burner out of the CPU and motherboard... The faster the CPU the better but you can do this on a P3 600mhz or equivalent. The DVD burner will give them higher quality and better compatabilty then VCD or SVCD would. If you cant squeeze in a DVD burner then a CD burner will have to do but make sure that their DVD player can play VCDs or even better SVCDs.
Video files are large so it would be nice to get a lot of RAM (preferably 512 and up, 256 can do the job though) and a fairly large hard drive or 2... at least 40gigs total.
Last but not least is CD burning software, Roxio easy cd creator is simple but only does VCDs not SVCDs. Nero isnt quite as simple but will do both formats. I would assume any DVD burner would come with DVD authoring software but i dont know how good it would be or what programs might do a better job (Roxio has some kind of DVD burning software which might be worth a look).
Think I got everything in there but I probably missed something...post back if you want more or more specific advice, Im sure other members will add their opinions too.
EDIT: The audio can get out of sync with the video if a low end video codec is used (low end MPEG or MPEG2 codec), if that happens you can work around that problem by only encoding 15min or so of video at a time, so you would have maybe 4 fifteen minute videos on a CD... you can set up a menu like on store bought DVDs so you can select which of the 4 you want to watch with the right VCD software. Oh BTW WinXP would be a good OS for doing this. Knew I forgot something.