Classical piano solo—Your one favorite performance and recording

Here's two nice ones

As mike in nc said, I can't give you just one - I have too many to choose from, maybe far too many. But just to be a little bit obnoxious, you mentioned Gould and Bach. If you want to hear a modern recording of the Goldberg Variations by a young and excellent pianist, you should hear Beatrice Rana's version on Warner Classic's. My preferred version of all available to me. :-)

FWIW one CD that gets a lot of play time from me is a compilation of very assessible but more modern (20th century) 'classical' music. 'Michael Sheppard plays Rogers/Hough - Barber/Sheppard  Crumb  Corigliano  Wild  Bolcom. 

If you can drill down your request to either composers, composition, or performers I, and others I think, could give you many specific recommendations.

John O'Conor's traversal of the Beethoven sonatas on Telarc is very good.  As are plenty of other recordings.

These recordings are still magic to me. They actually induced me to buy pianos that were, ahem, a trifle more expensive than my abilities deserved. Recording quality, of course, varies.

Rudolf Serkin -- Beethoven's Hammerklavier Sonata.

Phillippe Entremont plays Debussy.

Maurizio Pollini -- Chopin Etudes

Alfred Brendel -- Beethoven's Waldstein Sonata.

I saw all these guys in concert, too.

Vikingur Olafsson plays Debussy-Rameau