If your "classic bike" is a 10-speed bike (i.e. 5 cogs on the rear), forget it unless you have access to lots of free parts, have a deep wallet or really like your frame. If you have a 7-speed freewheel, there are chances it might be compatible with Shimano's 7-speed spacing, and therefore with 8-speed spacing (about the same).

You could then spread the frame to 126 mm and install a 7-speed Shimano freewheel or get a new wheel with a 7-speed cassette. It would then be compatible with 8-speed STI... providing you get a rear derailleur that is newer than 1996-1997. 15 and 20 year old derailleurs don't pull the same amount of cable (believe me, I have one at home).


There are two other cheaper options, however. These two options forego the "indexed" part, which is the most critical to get.

1. Get Kelly Take Offs. This is a bracket that you install under your brake levers, and that allows you to install your current shifter levers near the brake levers. Some like them, others hate them, but I have no experience with these.

2. Get bar-end shifters. Rivendell (http://www.rivbikes.com) sells SuperMix, as well as pods to install your current downtube shifters on the bar ends. You could also use modern Shimano bar-end shifters, maybe even an old set of 7-speed or 8-speed bar-end shifters. While they are indexed just like the STI, they also have a non-indexed setting which is compatible with any derailleur, number of speeds, cassette, etc.
IOW, you just need to buy the shifters and there are no other compatibility issue to consider.