As far as Gateways are concerned, start with Ghibli, then do a Shinkai film or two, before going into other anime. I find Ghibli tends to focus on bog themes with war vs pacifism, environmental custodialship, and the like in general whereas Shinkai delves more into the emotional exploration and development instead (like grief, love, longing, etc). If someone is able to enjoy and identify with both, chances are good you can successfully introduce them to other anime as well. My go to Shinkai films for newbies are Children Who Chase Lost Voices and Your Name.