Well, I guess I am being lazy for asking here...
To be honest, I was a bit overwhelmed by the plethora of choices I can make.
These "fundamental" genres of music are not what I am interested in learning at the moment, so all the selections seem equally appealing and unappealing. Nevertheless, I do realize that having them in my rep. is crucial for my development and success.
As for my stylistic weaknesses or inexperience, it's hard to say what they are...
I did receive a fairly well-rounded training, which gave me exposure to variety of styles. It's just that I have been entertaining myself with things like Kapustin and La Campanella, while my peers were painstakingly working on their Bach P&Fs and Beethoven Sonatas.
Having said that, I mainly wanted to know which pieces (out of the aformentioned genres) are considered "staples" for serious pianists since I have no real preference as to what to choose. Don't get me wrong, I did my listening homework. I just wanted a narrower spectrum of pieces I can decide from.