I prefer high efficiency 15" woofers with paper cones (most if not all of this segment of drivers use paper cones anyway), preferably crossed not much higher than in the 500Hz vicinity - horn-loaded if possible or in duals (per channel) as direct radiators. In this frequency spectrum and sensitivity range the specific configuration would seem to dictate the material used.
Above that frequency compression drivers fitted to large horns are my choice, and mostly a variety of metal diaphragms are used in such drivers - apart from BMS/JBL ring radiator variants where polyester is used. Aluminum, titanium, magnesium, beryllium, plastic or paper compounds (the latter of which would be HF-limited) - I couldn't say which material in particular floats my boat. Some prefer aluminum here for its claimed tonal prowess (think Vitavox S2 as a prime example), others beryllium for its upper extension and overall relatively smooth response (Truextent diaphragms come to mind), the PA/cinema industry for years has preferred titanium for its durability, some domestic users favor non-metal materials for what they believe is less harsh/more natural sounding to their ears, etc. Inclusivity be damned; it's about preference, implementation and the specific use.