In what order should I read the Touhou Project manga?
I heavily recommend reading the manga in release order, taking into consideration the release dates and plots of the official games. Most of the manga are standalone (with some exceptions) in the same way that the games are standalone to an extent, but keeping everything in line with game release dates will allow for better understanding of the plot context. 

Note that the manga focusing on the three fairies are directly associated with the Great Fairy Wars game, and note that Kasen did not have her first appearance in a game until WaHH had been going on for quite a while.

In general however, feel free to read them in any order (aside from the ones that are direct sequels, etc). Inaba of the Moon and Inaba of the Earth for example is entirely made up of separate comics, and as long as you are familiar with the dynamic of the characters, it is an enjoyable experience.