What are the best types of apples to use in Charosset?
Looking through recipes suggests a variety of apples.  Gala showed up the most, with Fuji in second, and McIntosh and Delicious tied for last.

If you want to go with the "source" of the recipe for Charoset, though, you'll want a sweet apple.  The recipe has its roots in Song of Solomon/Songs, and the verse that refers to the apples reads as:


  As the apple tree among the trees of the wood, so is my beloved among the sons. I sat down under his shadow with great delight, and his fruit was sweet to my taste.


So, for authenticity, go for a sweet apple, but Gala is the most mentioned apple in recipes online.