It sounds like you have two problems.
The first is obvious....your ABS has failed.
The second might not be so obvious. You say the brakes "scare" you. Is this becuase the pedal effort is high?
The pedal is soft?
The brakes pull?
The car shudders during brake applications?
Usually, ABS failure does not degrade the base brakes, however, there are unusual situations where a problem with the ABS modulator valve assembly can degrade base brake performance.
Recently "Corvette Enthuaist" magazine published a series of articles about C4 ABS diagnosis. I'd contact the magazine and see if back issues are available. It contains some instructions on how to diagnose the 86-89 ABS systems. Also, I'd buy the factory service manuals for 88 and refer to its ABS instructions as well.
As for the problem with the base brakes, we can't help you too much there until you, at least, answer the questions above.