I'd take a lot of opinions on Three Houses with a grain of salt, given how absolutely rabid a lot of people are about their feelings regarding certain things, but at the same time it's best to play through all 3 routes and there's not any clear intended order, so you can do them in whichever order you like.
One thing I'll note for you though since the game doesn't make it very clear: Whenever it is that you pick the Black Eagle house, in order to stay on the Black Eagles route and not go down the game's 4th route (which is not worth doing), you have to have Edelgard at support level C+ or higher before chapter 11, and then talk to her during chapter 11 and agree to go on a trip with her when she asks you. If you don't you'll be locked into doing the 4th route instead of having the choice to.