I found it was easier for me to get into the cadence and language of Shakespeare if I was already familiar with the story. After that you easily jump into to other plays. So as far as millennial/90s kid movies go:

If you’re a fan of She’s the Man (movie) then I recommend Twelfth Night.

If you’re a fan of 10 Things I Hate about You (movie) I recommend The Taming of the Shrew.

If you’re a fan of (or even remember) Get Over It I recommend A Midsummer Night’s Dream.

There are dozens more, but these are my favorite Shakespeare adaptations.