I had a similar problem in my 96 SER..when cold..it would make this loud hideous squeal ..First i thought it was my belts slipping that was making the sound..but when i changed my belts with the new pullies the sound was still there..For some reason the late 95-96's have the bad hitachi starters..model#23300-63J01...The one that is recommended for replacement which is the one that i have now is #23300-63J10 its a Mitsubishi unit and its 147 bucks..from Courtesy.
Well mine does it. Does it most of the time. Like a second of squeal most every time i start the car. Dont think there is anything to worrie about. George said its from the starter brushes wearing out. He said it has done it for 100,000 miles on his old engine and nothing bad yet. So until you cant start your car I wouldnt worry too much about it.
My '94 had the same problem. I had the starter removed and lubed (the shaft is not retracting properly) and it's worked fine for 120,000 miles since. Definately get it fixed- you'll wear the flywheel out eventually. The fix cost about $40 for labor.