My country is a constitutional monarchy in theory but a parliamentary system in practice. France, Italy, Poland and Russia all are semi-presidential systems yet are politically nothing alike. What a system is called barely gives you information about what it really is.
As far as I know the Netherlands are a parliamentary (which necessarily means constitutional) monarchy.
I don't know what to say about eastern Europe.
But the question is what you think works (or could work) best. I know that republic and monarchy are neutral terms but the type of government says a lot about a country. But I agree, it is kind of hazy.
The problem is if you talk about the "real" form of rule, that the definitions are not very clear and there would be arguments about which form of rule a country would have.
The options I made available are clear and understandable even though they are very theoretical.