"Glue" app to specific screen

I have multiple displays, and I keep having to move apps around to where I want them, even though I JUST DID IT when I opened the app the last time!

I know there are ways to script this, with Slate or probably even Applescript, but I just refuse to believe there's no way to just let the OS know that Plex belongs on screen #3, Chrome on #1, and AirMail on #2!