Nice find, I get roasted all the time for saying cars like yours can be found for 5k. White is one of those colors you are indifferent to til you own one or two.
Look clean when they are dirty, stay cool inside and noone keys them.

It depends what you can live without for that kind of money. Be realistic about what the C4 is, and what it is not. (It is a toy; it is not an investment.) If you don't care about nice interior, air conditioning, radio, or other things unessential to a good driving car, then sure get a cheap one that runs good and have some fun. And consider how to fix those things that you want fixed -- either you/friends will do it for cheap, or you will spend real money paying someone else to fix.
If you want nice car that is mostly/fully functioning, I suggest you save up about $7000-8000 first. It's far better to spend more on a good car up front, than to spend less on a fixer-upper and then spend extra fixing everything... and end up at the same place anyway.
Also, you can expect to pay $1500-2000 more for a manual transmission.

Question. You are buying my car. The interior isn't good, the paint isn't the best either, the AC is dead for some unknown reason and the radio is just as dead. Many of the things aren't working well. How far behind do you think the motor and drivetrain and suspension is when you see an owner like what I described let his car go to hell?

Given its condition, I would not spend much money on your car... but it runs so maybe it matches the OP’s budget and goals perfectly. So you are asking me to play "what if" with the condition of the drivetrain and suspension? You may have rebuilt part/all of it, and just haven't gotten around to restoring those other parts yet… or never. And if rebuilt, it may have been abused or well kept... who knows? Do you have receipts or service records? There is no real answer for your question, only guesses. Yes you are correct that buying a used car is a gamble, especially a 25+ year old sports car. I just don’t think it is useful to play the "what if?" game while doing nothing to answer the OP’s question.

The OP did not state his intentions for the car he might buy. So I'm just saying, if he wants to spend a few thousand on a worn car (which still runs and drives) and have a little fun (which may be exactly how you used your car, now for sale), perhaps a car with a few liveable flaws would be a good choice, given his budget. Liveable being defined by each individual, I left the question very open for him to decide for himself. These drivetrains are generally pretty tough, with a few well-known exceptions.

I know if I was in the OP's position, with $3-4000 to spend on a fun car, I would certainly be willing to look past faded paint, an inoperative radio, maybe some loose interior trim pieces and many other items that do not seriously affect my enjoyment of a Corvette... considering the budget. That was really my point.

My point is that I am not playing "what if" in this case. I am going off the assumption that if your car is not looking like it is well maintained on the outside, I assume the condition of what I cannot see like the engine and drivetrain, suspension and all that won't be well maintained. If it is, well, that is a bonus but I am going in on the assumption that the unseen parts are in about the same condition as the visible parts.

I have a friend that wanted to sell me his 84 , that wouldnt start, for 25 hundred. He had thrown all kinds of new parts t it, still didnt start. I almost jumped on it, cause it was otherwise in fairly good shape. h\ I didnt sta on top of this and he sold it for 15 hundred. guy that bought it is driving it around now. Not sure what was wrong, have to wait to see friend again. Just an idea for you, lots of deals to be had out there.