My personal recommended reading order:

Hinamizawa Bus Stop (HBS)
Outbreak
Kamikashimashi (requires the above to be read)
Mehagashi (requires the above to be read)


Hinamizawa Bus Stop can be read at any time - it's seen as the chapter Higurashi was based off, and doesn't have much relevance to anything else in this game.

Outbreak can be read before or after HBS. Do keep in mind that the 'Kamikashimashi' chapter is a continuation of Outbreak's plot. It requires HBS + Outbreak to be read beforehand.
It may be smarter to read Outbreak after HBS to instantly unlock the chapter. Personally, this'd make it nicer to read, as the flow of the plot wouldn't be interrupted by HBS.

Mehagashi is like Hinamizawa Bus Stop - it doesn't have much relevance to anything else. The game requires you to read Mehagashi as the last chapter (after having read all the previous chapters mentioned).

There is then an extra afterparty you can read, followed up by lots of staff rooms. If you want to read these, the order really doesn't matter.