Is it worth buying a second hand classic road bike for commuting?
A (decent) bike from the '90s would not be significantly different† from (a decent) one only a few years old except for a small weight difference and possibly lacking brifters, which are de facto standard on road bikes these days. This statement is of course excepting top-of-the-line superbikes made of carbon fiber and dragon's blood.


Check it for stuff like rust in hard-to-see places (small bolts etc.): This is a good sign of how well (or rather poorly) the bike was taken care of. If there is no or minimal rust, it's probably been taken care of well enough.
Look over the frame for any signs of crashes: Big dents, cracks, fissures, etc. 
Check if the headset wobbles or not: It shouldn't, and if it does, it might need to be replaced, which would be very expensive.
Check how worn the chain is: If it looks horrible and probably has never been changed, that's a warning sign.
Check the teeth on the front chainring(s): If they are starting to look like shark fins, the chainring will need to be replaced. 
And of course, just ride the thing and see how it feels.




† "Significantly different" means from a mechanical/engineering perspective: IMHO, some of the ugliest bikes I've ever seen were from the '90s.