Which game to play first for best experience?

[Rising Gale]

Which should I play first? Momodora moonlit Farewell or Momodora reverie under the moonlight first?

[NoxenToxicar]

Most people would recommend playing Reverie Under the Moonlight first. Chronologically, it takes place before every Momodora entry, and is the game that Moonlit Farewell builds on.
The events of every Momodora game in between the two is told via notes in Moonlit Farewell so you don't have to worry about that if it was a concern.

[Hotel Security]

It doesn't matter. They have very light ties to each other. Play them in whatever order.