To process granulated white sugar and raw sugar to superfine consistency, process them together for about 1 minute in a food processor.
For the filling, 1/4 cup of sugar will yield a fruity and not very sweet filling. If you prefer a sweeter taste, add up to another 1/4 cup of sugar - 1/2 cup total.
Bake one disk's worth of hamantaschen at a time. In the time listed at the top of the recipe for the "cook time", I have assumed that you do not have a double oven and therefore have to wait until the first batch is done before you can bake the second. If you have to re-use pans, make sure they are cool to the touch before putting the second batch on them. You can run them under cool water and dry them to cool them down quickly.