Do you mean reading stuff in classical japanese, or just classic lit? 
I’m not so interested in Genji since (a) I’ve read it in English and (b) I’m not super-interested in reading it in a translation into modern Japanese. But classics in the “modern Japanese literature” sense might be interesting (I’ve read a little Soseki and Tanizaki, for instance).
Speaking of Tanizaki, we’re about to start reading 痴人の愛 in an informal book club in a few weeks.
