The Rivals: A courtship comedy involving multiple lovers and a couple of disguised identities. Still holds the stage, in part because of the presence of Mrs. Malaprop, whose habit of inadvertently using soundalike words introduced a new variety of verbal humor. (A fine modern example of a malapropism, which stuck in my mind some years ago, is "tuna camisole.")
The School for Scandal: A classic marriage comedy. Its basic situation, that of an older man who marries a young woman from the country in the hope of acquiring a wife not susceptible to the wiles of city society, is akin to Molière's School for Wives. The context for their wrangling involves a gaggle of gossips led by Lady Sneerwell, as well as the Surface brothers, one thought a wastrel and the other an exemplar of fine upstanding moral sentiment—and then there's the rich uncle who visits in disguise. Have you heard of "the screen scene"? It's in this play, and it's one of English comedy's most ingeniously plotted scenes, which I won't describe in case you haven't encountered it.
The Critic: Wikipedia labels this a satire but also a burlesque, two things that are far from identical, and at least one Goodreads reviewer managed to take it as a critique of critics, which misses a lot to say the least. Suffice it to say that The Critic makes fun of the theater business, much as a number of modern Hollywood films make fun of the film business.
I read those plays in search of inspiration for a project of my own. I skipped The Duenna, Sheridan's libretto for a comic opera, and A Trip to Scarborough, his adaptation of a Restoration comedy by John Vanbrugh called The Relapse.
The introduction, by Michael Cordner, is valuable. His numerous annotations, however, regrettably appear as endnotes rather than footnotes; what's more, they may be useful for young students but will be almost totally unnecessary for anyone acquainted with the earlier stage of English language and literature in which Sheridan's work is situated.