“Which are more important, the mountain and water stars, base star, yearly or monthly stars?”
The are many schools in Feng Shui that makes use of the 9 Stars e.g. Xuan Kong Fei Xing, Purple White etc.
Then even with the Flying Star schools, there are many lineages and along comes many ways to interpret the stars.
For me, I place greater emphasis on the water and mountain star, followed by their combinations.
I used them to decide the optimal position for the main door, bedrooms, stove etc in connection with the external environment. For example a good bedroom should have a good mountain stars or mountain star/water star combo plus a “mountain” feature outside e.g. higher land, hills, forest etc.
Next is the combination of the water and/or mountain star with the base star. For example I have a good water star but not a good mountain star. However I have a good base star. I may still consider using this sector for example for the main door especially there is a suitable “water” feature e.g. lake or open space outside.
The yearly and monthly stars are used in collaboration with the water, mountain and sometimes base star primarily for current year and current month predictions.
For example if an auspicious current yearly star meets a current auspicious water star at the main door, we can say that there is likely to be auspicious career/wealth opportunities this year for the occupants in the house. E.g. promotion, business success etc.
The same methodology would apply for monthly prediction with the monthly star.