By the way, I've done this upgrade myself so I know what it entails. I ride a 620 of approximately the same vintage with modern parts.

cyclintom is mostly right, but getting an eight speed setup is easier than he implies. Really, all you need that's "eight speed" specific are shifters and cassettes. MTB 8 speed cassettes are still very common and 8 speed barcons are also widely available from a number of sources.