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Probably the most critical area of a C3 is the frame and birdcage. If these areas are heavily rusted or rotted you are looking at a lot of work and big bucks to fix. Unless the car has been restored you probably will be looking at replacing the brakes and at least doing a major tune up on the engine. If the car is a stick you should check the clutch and the operation of the shifter and tranny for wear. If the car is an automatic check for leaks and check the fluid to see if its burned. Next I would look at the power steering system. This area is problematic because of leaks at the control valve and ram. Look for wet areas. Make sure the radiator and fan shroud are intact and check the coolant. Take a look at the paint. A good paint job can run $10K so don't think you can get a quickie paint job for $499. You won't be happy with it. Also check the body for stress cracks along the top of the fenders and the corners of the hood. Also look at the condition of the front and rear bumpers. These were urethane and are prone to waviness and cracking. If you need them replaced it will cost to buy the parts and have them painted to match the car. I'm sure others will chime in but this is what I would look at first. Good luck and welcome to the forum.
Welcome to the forum. With any car 30 years old there's lots to examine.
Particularly the frame. Get it up on a lift and look it over carefully. Use a mirror and poke and scrape to determine soundness. Power accessory systems are another area, work them all. Does it run hot? I'm sure others can add to this but thats a start.
Good luck
There are several detailed "buyer's guide" or "what to look for" threads, which should be easy to find in a search. There's also a pretty good "buyer's guide" book available.
The frame and birdcage (metal body structure) are the two big areas to watch out for...especially the frame kick-ups in back, the windshield frame and the rocker channels. Corvettes may be made of plastic, but they do rust...
Rust is the enemy. Especially in the birdcage - that's like cancer in the old vettes. Behind the rear wheel well is bad. Check the body mounts for rot. Also under the radiator tends to get rusty and eaten through.
Trim pieces and all the little things cost $$$. Getting parts for a Chevy 350 to make it run (if you're not worried about date codes and factory originality issues) is not a big deal. If you're looking for an original car to restore to factory specs, then get yourself the NCRS Tech. Info & Judging Guide and put your eyeballs on some cars being judged at a local meet first. One day spent doing some HW will save you a lot of headaches and money later.
Most of all have fun! Once you've got the car, the real work begins. ~Juliet