Yeah for audio, definitely just line in. If the retro PC's sound card has it, use the unamplified output jack. Might be called Line out, or might be Speaker Out if the amplified one is labeled Headphones. If you want the best quality record it in lossless FLAC.
For video, you might be able to find an older PCI or AGP TV tuner card designed for recording cable cheaply. One with either coax, svideo or composite, and use a VGA>svideo and a svideo>whatever the card has adapter. Won't be great quality, but I'd imagine it'd be decent enough. I have a couple old Hauppage PVR cards and a Radeon All in Wonder 8500DV that I've thought about using for this. The thing would be to make sure the software for them can actually record, not just work as a tuner. If you wanted to spend a bit over $100 you could get an Avermedia Game Broadcaster HD; I've been wanting one for a while. Captures anything from 640x480 to 1080p at 60hz, BUT there is a way to make it record lower resolutions as well, so you can use it for DOS stuff.
EDIT: Shoot just realized you're thinking of using your laptop for this; I was going off the assumption you had a desktop you could use as the recording machine. Sorry! I think there are some usb capture devices, not sure how cheap they are though.
Found this one, looks like it can record, and it has a cable with composite and svideo connections. http://www.amazon.com/Kworld-Tuner-V.../dp/B00AEK5WRC Probably not the best quality but it's pretty cheap. Then you could use a cheap vga to svideo adapter with it, like this one: http://www.amazon.com/S-video-Conver...rds=vga+svideo