I could be wrong but I think the OP was saying that his OVERALL musical tastes are pretty eclectic, not that his tastes WITHIN the classical genre are eclectic. So maybe start with recommending large scale orchestral works and piano compositions that are a bit more accessible than Part, Stravinsky or Bartok? Showing my age here but my interest in classical music was stimulated by the film "Children of a Lesser God". There are two points in the film when William Hurt tries to decompress after a long day and puts on the Adagio from Bach's Concerto for Two Violins. I had zero exposure to classical before that moment and it sounded so lovely I went to the local record store (Melody Records Dupont Circle in DC) and bought Trevor Pinnock and the English Concert's most recent recording (on CD). I moved back to NJ months later to work on my thesis--hours a day for nearly a year--with WQXR on the radio and the listeners guide on my desk. Every time I heard a piece I liked I highlighted it in the guide and then brought it to the record store with me to guide the building of my collection.
