What bars are you running?
is it really a fixed gear or did you just swap the 6 speed freeewheelfor a BMX freewheel on the stock wheel and make it a single speed?

Do you have the original derailleur?

If you are running straight bars and your original wheel I'd consider going with a 7 speed grip shift or thumb shift with a Mega range MTB free hub and a Derailleur. New you could be up and running for under $60. used you could probably hit the local CoOp and be done for under $15.

80's bike is going to be a 126mm spacing where a modern 9 speed is 130mm. Older steel frames You can force it in but be careful it spreads equally on both sides or it will dog leg (ride sideways).