What is a good set-up for the board of directors/executive committee of research institutes?
There are many examples of University research boards and their makeup (as I'm unsure what your research institute focuses on, it's difficult for me to pick a similar one, but it's easy to find examples on the net) however I'd definitely recommend a few things from my experience on non-profit boards.

Firstly, all those influenced by your decisions should have a representative. This means students in your case - it's vital to stop problems down the line.

Secondly, wherever possible, all members should be elected as impartially as possible. This isn't always easy, but it's an important step in proving the high standards of the board.

Lastly, realise that a board of any kind tends to get into cliques. Anything you can do to stop that is important. Examples to stop that would include a rotation of positions, or setting tenure lengths.