in part it depends on what you like. which i know is maybe a dumb obvious thing to say so apologies if it is. there is a spectrum of more or less accessible to newbies, but there’s still a lot on the “more accessible” end.
so anyway, shakespeare generally wrote three kinds of plays, tragedies, comedies, and histories. the histories in general can be pretty good, but more difficult to get as much out of them if you aren’t already kinda a nerd. but other than that there’s lots.
a lot of ppl say start with hamlet, but from what i’ve seen it’s really a “love it or hate it” sort of play, kinda like the theatre version of bleu cheese.
so here are my suggestions
Macbeth - Short and gritty and edge of your seat. a bit of a mystery/thriller about prophecies, backstabbing, and the place of violence in a warlike society.
Romeo & Juliet - drama and social commentary and romance. i didn’t put the romance first because it’s not just about that but it’s there. makes me sniffle every time
Julius Caesar - Politics and drama, and a lot of people read it as homoerotic and kinda gay. Rather blunt and manly and stony imo, but some really beautiful well done speeches.
(also if that ancient (homo)eroticism sounds like your cup of tea you might also try Antony & Cleopatra or Coriolanus)
Midsummer Night’s Dream and the Tempest - Fairy shenanigans
Much Ado About Nothing - Romantic Comedy and Social Commentary and smartass flirting
As You Like It and Twelfth Night - Romantic Comedy and Social Commentary and crossdressing.
Richard III - technically a history, but full of villainous, thriller-ish, dramatic shit similar to macbeth. NOTE: THE REAL RICHARD III WAS NOT LIKE THAT. IT IS NOT HISTORICALLY ACCURATE. IT”S BASICALLY ELIZABETHAN PROPAGANDA BECAUSE SHAKESPEARE’S PATRON CAME TO POWER BY KICKING RICHARD”S PEOPLE OFF THE THRONE. AND HE KNEW WHAT SIDE HIS BREAD WAS BUTTERED ON. it’s still good though, maybe it’s even more interesting knowing it was a bit of a propaganda piece.
Shakespeare’s plays are written in a slightly earlier version of english called early modern english, so maybe not the english you’re used to. but if you’re already reading lit in multiple languages, that can help.
Definitely watch them if you can, plays were written to be watched and it does make the experience a lot better. there’s a lot of versions floating around on YouTube if nothing else.
here’s some ppl on tumblr that write interesting maybe helpful stuff about shakespeare
http://motherfuckingshakespeare.tumblr.com/post/89614764405/how-to-shakespeare
http://noshitshakespeare.tumblr.com/
http://dukeofbookingham.tumblr.com/tagged/shakespeare/
http://arisefairsun.tumblr.com/
http://shredsandpatches.tumblr.com/
also, you might want to watch the tv series Slings & Arrows which is up on YouTube, it is a drama/comedy series following a shakespeare theatre and goes well with reading the plays.
Here’s a video about Shakespeare’s english (early modern english)
https://www.youtube.com/watch?v=gPlpphT7n9s