IMHO, that's a very good price for a low-mileage 1987 convertible. I have owned three c4s over the last ten years, and although they have their share of potential problems, I wouldn't say they need "constant tweaking". My current ride has been the most reliable c4 I have owned.
Right off the bat, I must say the single most frustrating thing about the c4 is the alternator. I have had more alternator problems with these cars than any other problem. So if you buy the car, I strongly suggest you find a heavy-duty alternator from somewhere, either Ebay or a local alternator shop, because I can say this with one hundred percent certainty: you will have alternator problems. And it goes without saying that you will want the best battery money can buy. Those two items have been the cause of about 90% of all my problems.
That said, it's a pretty simple car to work on, and easy to understand. I suggest you purchase the service manual (Ebay again). Some things are more difficult to service than others, but you can do a lot of the work yourself. Brake pads and rotors are easy to change, for instance.
Here's an excellent site full of pre-purchase information:
http://www.c4vettes.com/prepurchase.htm
If the car is in good shape, it is definitely worth the money. It will be the ride of your life!
Good luck!