Transom open. NO, just no to shutters.

I would leave the transom open, too, unless you need privacy or are going to keep the draperies to pull if privacy/darkness is needed. But is that a sliding patio door? Can you even use shutters on those?

eta: I did see some pics with the transoms covered with shutters and it's a less fussy, less cluttered look. Good to know about sliders; I've not seen that done.

I don't think shutters will look right with the dimensions of your windows. Definitely leave the transoms open. I would leave the drapes, and in the windows where you need privacy, add an unobtrusive shade to pull down when needed. Shutters remove a LOT of light, even when they are open.