Rule number one...buy the best car you can afford. I've owned a Darrin and it was one that was missing a few vital pieces. I spent more to have one casting made than most folks spend on an engine rebuild. Make sure whatever you buy is complete, or at the very least, you have access to what's missing.
Rule number two...if you're after an "authentic" car, make sure the VIN and body number tags are intact and that the paint and trim codes match the tag. Yes, the car can be repainted back to it's original colors but if you're buying a restored car that's the wrong color, that's an expensive mistake. If you're not after "numbers matching", then at least make sure the body is in good condition. They are fiberglass and prone to stress cracking in several locations including beneath the doors and between the top and trunk lids.
Rule number three...check the frame carefully. The Darrin used a Henry J frame that was heavily modified and over the years, rust and stress cracks have taken their toll on many.
Knowing all of that, again, buy the best you can afford. Prices are all over the map, from unrestored cars that are basically a body, frame and title, to nicely done cars commanding top dollar.
I'm sure others will chime in with hard-learned advice!