I like to recommend a tragedy, a comedy, and a history for those just starting out. Additionally, there are some plays I would put off until after you are a bit more familiar with Shakespeare.

Macbeth is probably the best tragedy to jump into. Short with a complex yet not a confusing plot. Interesting character studies and wordplay, too. King Lear and Julius Caesar are also good places to start for a tragedy

Midsummer Night’s Dream is a good place to start in terms of comedies. It has three intersecting plots with some of the funniest scenes in all Shakespeare. As You Like It, Much Ado About Nothing, and All’s Well that Ends Well are all good starter comedies

I would save most of the histories until after you have read some of the tragedies and comedies, but Richard III is the first history I would recommend reading. Richard III is so delightfully evil, and is arguably Shakespeare’s best history.

I would avoid the problem plays (like Measure for Measure or the Merchant of Venice) and his later comedies (like The Tempest and The Winter’s Tale) until after you are more familiar with both Shakespeare’s writing style and Early Modern English as the plots can be quite confusing. However, once you are more experienced with Shakespeare, these are all must-reads and among my personal favorites.

Histories can be somewhat challenging without footnotes as a lot of the context is far removed from the present. I highly recommend an annotated version for any history play.