I love the 560SEC. It is a big, beautiful, classic, and a pillarless coupe. It is old school Mercedes at its best.
The main thing to look for in my opinion is that it doesn't have dents, that the paint is perfect, and no rust. Sunroof should work. And that the interior is in good shape, meaning the plastic parts, door trim, carpet. Radio is not important, can be easily upgraded including speakers. I would even buy one with a defect engine or transmission if these criteria are met.
Now the drawbacks: The seats are not great and if the springs are broken, you never get them 100% again. The throttle response is not like a modern car, the engine drinks fuel due to the 2 valve design combined with the mechanical Bosch fuel injection and old electronics.
I would modify the following:
Get Recaro front seats from lena-shop in Germany, and the leather for the rear seats (very cost effective and great quality).
Get a suspension kit - Bilstein B8 with H&R springs or CEIKA (adustable). Get rid of the self leveling rear part. It will drive beautifully with responsive steering.Change the transmission to 5-speed 722.6 with Ole-controller. You can get it to Lexus level (I have a LS430 and that auto-transmission is perfect). And you can install paddle-shift if you like.
If you still crave for better throttle response and fuel economy: Change the engine fuel injection system - M117 to EFI or put a M119 engine with EFI into it. Now, you have modern throttle response.
Don't spend any money on AMG nonsense.
The beauty of the 500e is less work, a more modern car.
Seats - I don't know, but they don't look great either. I guess they are similar to the 560SEC version.
EFI is already there, meaning you have good throttle response and fuel economy.
You could change the transmission to 5-speed.
Suspension - should be fine.
Summary:
To get the 560SEC to drive like a modern car, you will need to invest money. The real beautiful 560SECs are the European versions. If you can get one, take it. You will pay a lot of money for headlights and bumpers later if you decide that you want the Euro look (the Euro lights are actually better).
The 500e is a modern car out of the box except for the transmission and I guess the seats are not much better than 560SEC seats.