Is there also a recommended route order?

Nope. Just meiya and sumika routes. The rest you can read if you want. Side characters do reappear later on.

Doing Sumika and Meiya ("near side") routes is required to unlock Unlimited, but you should read the other three routes ("far side") as well before you go into Alternative.
In terms of recommended route order, do Sumika and Meiya first (either order is fine), then do Meiya's route in Unlimited. After that I'd suggest completing all of the remaining routes before moving on to Alternative, but you should at least do the Extra routes, since they introduce characters you'll want to know going forward, and I'd recommend doing Ayamine's Extra route after Class Rep, not before.

Main routes are the most important but every route helps make you feel more attached to each character and some introduce characters that will come up later

and the side routes are pretty good too