I think it makes sense to know more than just the number of rooms before the appointment with the architect.
Full agreement
I believe it is easier for an architect to understand what we want if there is an example floor plan.
Don’t take just one floor plan, but several and explain what you like about individual aspects. The architect can then piece it together. Also show pictures of rooms and exterior views that you like. Describe a typical workday, variations of a successful evening, hobbies, a nice day off in winter, in bad weather, in summer, in heat, in social settings, in quiet…, describe routines and preferences as well as dislikes. Let the architect translate this into architecture. If he or she is not interested in this, find another one. You could gain interest as follows: “Would you like to design and build the right house for us with great creative freedom?”