in terms of what knowledge and skills... this is a very logical question! i used to rely on my teachers for most of my info (out of laziness - and, i thought, a shortage of time). now i realize time shortage is what all of us deal with (teachers included). so, it never hurts to learn about periodicals. that way, you are up to date, and people say 'wow, you really know your stuff' even though you are quoting somebody else who just researched it. there is so much to be learned even though it is history. always someone discovers something new. you don't want to be requoting textbooks from 20 years ago (as i was want to do - until taking more classes). just as with new math (can't stand the stuff-but have to understand it better someday) you won't be able to keep up with the times. things are very much 'if you can explain it, you can do it.' so, if you are playing the preludes without the fugues - tell them why - and it's ok. personally (i do like the old textbooks) people just want the basic facts and then something perky or interesting to go along with it.
What perhaps interest me most of all, is that certain pieces quickly lead to dead ends, while in others (Bach, Schumann and Beethoven come quickly to mind) it seems that the more you research the more they unfold.
- background information about the composer, time period, that specific piece if possible, the type of music the piece is (sonata form, fugue, etc.)should you have....- the melodic line memorized by itself?- the chord progressions memorized by themself?https://pianoforum.net/smf/index.php/topic,7720.0.html