My Shakespeare class in college was based around performing a play at the end of the semester. We read about half a dozen plays, but the bulk of our work was based around preparing to perform Hamlet (each semester, a different play was performed, with fall being Comedies/Histories and Spring being Tragedies/Romances).
The big challenge is that a lot of plays are rarely performed. I had the good fortune of hearing an interview with Kenneth Brannagh where he talked about how Shakespeare is better experienced by watching a performance than reading a text and he made an aside about how it’s unlikely you’re going to get to see Henry IV part II performed and then spotting that there was a free performance of that exact play being given at the Chicago Cultural Center. This turned out to be part of a series of staged readings of all the plays. I missed the beginning of the sequence, but stuck around to the end. One of the coolest moments of this came when I was attending a play at the Goodman Theatre which had the actors interacting with audience members during intermission and one of the actors in the play recognized me from the audience of the staged readings.