The most commonly used SNS for instant messaging in Japan is called Line, so I would download that for starters. I find Instagram usage is pretty high too, for sharing your standard travel snaps and slice of life content. If you don't already have any Japanese friends who you're messaging on those platforms then I would suggest an app like HelloTalk or iTalki (language exhange apps), list your Japanese level as basic (i think they allow you to say basic/intermediate/advanced) strike up a convo there and then move across to Line/Insta. The italki app is fine and all but it's artificial.
and that the average Japanese person is not consuming English-speaking media
Unfortunately this isn't my experience depending on age-bracket. There is a sizeable portion of Japanese people (I'm going 18-35 here cos that's the range for my friendship group) who do consume marvel/disney. Disney in particular with Disney World and Disney Sea being popular theme parks. Universal Studios in osaka too. Idrk what IPs are which but to say that western media is a cornerstone of pop culture. That being said there's a lot more domestic media they'll watch relatively speaking, and a decent amount of kdrama.
If there were a single series that you could watch that would have the broadest cut-through as a leaping off point, I would recommend Conan the detective, which has been an anime mainstay, demon Slayer too more recently.
Idk these are broad generalisations I'm typing up on my lunch break