Originally Posted by
Val the Moofia Boss
While each arc ties into a larger narrative, each arc ultimately tells its own story with a beginning, middle, and end.
You can play each arc without having played the last game. The Crossbell games have maybe half an hour of cameos from the Sky arc over the course of 100 hours.
A couple characters from Sky appears in CS1+2 as background characters.
CS3+4 brings back characters from Crossbell and Sky as supporting characters, but the focus is on the protagonists native to the CS arc. Also, if you've played FC, you'll be pleasantly surprised to see a core theme of that game come back in CS4.
Obviously, there is enjoyment to be had in seeing how the world and its characters change over the course of the games, but if you want to play a specific game, then go right ahead.