He should only work fine and not much more than 500 euro cost needed by me
And what is the question?
For 500, - there are only used, and rather older. From private is risky, because you are completely unaware, so look around at maconline.de, because you should find something akzektables in the price range and get 12 months warranty.
Of course you have to get you a used Mac. Look for a MacBook Pro from 2011 onwards. For him, there's still the current operating system.
These older Mac computers are still good to use. Let me confirm that it works properly and that the battery is not too used. The power supply should of course be present.