Are all notes of the same importance? Commonness?

No.  The closer to the center of the piano, the more likely.  White keys are usually easier to play overall, so they’re more commonly played overall.  (Yes, there are LOTS of pieces of music that require black keys, so they’re by no means forgotten.)  Also, the Key of C Major is the “easiest” to play in, since it uses mainly (and in some pieces, only) the white keys.  Going further, the note c is the “strongest” note in the Key of C Major; and going even further, Middle C is probably the most likely single pitch to be played at all.

Music is a complex art, and there is plenty of need to learn about other keys, etc.  But while we’re learning, we have to break down the task of understanding the piano, and it should be comforting to know that a small handful of notes will give you plenty of music to make fairly fast!