It's really up to the individual how they want to learn. But I think the best way to go is with low-colour counts. If you have a grasp of traditional art knowledge as Helm and Elk have noted (and I concur!), then I think the best approach to picking up pixel art is working with some of the restrictions of old systems such as NES/Famicom, Commodore 64, or Gameboy Classic.
Such restrictions enforce concepts of colour recycling, contrast control and readability. As Helm has remarked in
this superb thread these restrictions also force you to deal with critical pixel cluster arrangements, and build up ideas of what arrangements of pixels work within particular contexts, and which don't.
As a personal suggestion, I don't recommend working with palettes much over 16 colours for pieces; it's too easy to get sloppy with palettes and keep racking on extra, unnecessary colour indices in place of practising good colour economy. 16 gives you lots of freedom, but still demands efficiency, imo. Can't really make clear suggestions for tilesets/mockups. I usually go with a preset global palette with those. But I suggest having a go at some of the system restrictions with tilesets.
As I said, it's up to you.