I had a 1987 Corvette that was a 4+3 manual and a Z51. Unless it is a convertible, $16,000 is waayyyyy too much. That car will never be collectible, even though the Z51/4+3 was rare. I sold mine with 80,000 miles on it for $5,700 about a year ago. I bought it 5 years ago with 40,000 miles for about $10,000. It had Bose and the defroster/side mirror defroster, and the solid top. That's what I would say it would be worth with 24K on the odo. I might go to $12K since you said it was loaded (it would have to be perfect, though). Once you start getting around $15K, you're talking early 90's LT1's. The low mileage is nice, but if it's real low you can almost guarantee when you start driving it daily that little things like the battery and alternator will crap out. Low mileage can be sort of a curse too.
Nice things about 1987:
- Anti-lock brakes
- Aluminum heads that added 10hp
- Roller lifters that reduce drivetrain losses and lifter/cam wear
- overdrive button moved to the shifter top instead of a switch on the center console. This is just cooler and easier to use.
1988 was the last year for the 4+3, and that year saw bigger brakes and 17" wheels. The 4+3 is a nice tranny, and it doesn't have the skip-shift crap, but the overdrive unit can go bad. I think mainly it's from neglegence. It requires the maintenance of an automatic (drain the fluid, replace the filter every 30,000 miles). It doesn't have a torque convertor or anything so it doesn't add drivetrain losses. And it's cool. If you punch the gas, it will downshift from overdrive on it's own. There was a very collectible 1988 Corvette: the 35th Anniversary. It is one of the most beautiful Corvettes ever IMO. One of those with under 75,000 miles would be about $15-16k and much more worth the money IMO.
However, a 1987 is an excellent car. That 345 lb-ft of torque is amazing. And they are quite easy to work on. There is a ton of aluminum and it's really pretty modern considering it's age (tilt/telescope wheel, ABS, intermittent wipers, cupholders...). I miss my car sometimes, but we just didn't have room for it (which is a shame because it wasn't about money. It was worth much more to me than it was worth as a car).
Things I would look at (in addition to all the normal things you check when buying a used car):
- check the weatherstripping. It is quite expensive to replace, and the top will leak if it's cracked. Parts alone are over $1,000.
- check the tires. Find out how old they are. It's possible they are original since you said it has 24K. This would be quite dangerous to drive on if they are. The rubber will harden and have small cracks all over it. Look for the DOT manufacture date. If there isn't one, it means they are at least like 10 years old since they started that in the early '90s.
- make sure the overdrive unit in the tranny will shift from high to low and back. These are the weak spots in the tranny, but usually from lack of maintenance. They need the fluid changed just like an automatic, and the level needs to be checked occasionally (which requires going under the car).
- check for cracks in the paint, especially on the hood. This is common from the fiberglass flexing, but you just want to be aware of it ahead of time. It's ok if it has it, you just want to know.
- since it is so low mileage, check the maintenance records. If they never flushed the radiator or changed the tranny fluid because of the mileage, you just might want to be aware of that. Or if the oil was only changed like every two years because of mileage, you'll want to know that too. It might be a reason to offer less, not necessarily a reason to pass on it.
- check the shocks to make sure there isn't oil sprayed out from the middle. The Z51 shocks last much much longer, but when they go you will see oil spray from the shock. They will almost definitely be dirty, but you want to look for oil.
That's all I can think of now.