I think the repertoire hardly make it to Classical top ten something. But taste is a difficult word, just try it. Repertoire like Dvorak American quartet I think can attracted new listener quite easily.
Beethoven's string quartets were actually some of the first things I listened to when I started getting in to classical. I see all this talk about how they're "difficult to understand", but I don't really get it, they all sound just fine to me! And only one way to find out if you'd like them...trial and error
When I started listening to classical, I only listened to orchestral music. I liked the orchestral colors. I thought string quartets and piano pieces were too monochromatic. After I got into classical, I tested the waters and found I actually liked other genres.
Something must be acquired; I don't know that it's 'taste'. The new listener has get used to the sounds the instruments make, both individually and together. When I started out (it was with Beethoven's Op. 18 set, played by the Guarnieri SQ) I thought it sounded like everyone was slightly out of tune. As it turned out, they were not.
I spent a fortune on deodorant before I realized that people don't like me anyway.
When I got into Classical Music I was almost only listening to String Quartets. I started with Beethoven's late ones and then I realized that I discovered awesome music. I guess it was quite natural for me.
Either way, I really suggest that you try and "acquire" that taste. There's truly great music to find there!
On facebook I recommend a daily piece to my friends, and I have refrained from chamber music in general unless it's a piano piece that I have played before. I usually stick to orchestral things. Thanks for the input.