Thinking on this, I believe Pirates is one of the more straightforward plots.
I had to literally construct a diagram to make heads or tails of Yeomen; It didn’t help that I only had an audio version.
Topsy Turvy is damned odd, btw. Just be prepared.
I like Mikado, Patience, HMS Pinafore and Pirates of Penzance. The Gondoliers is also quite funny. The operettas are supposed to be satirical and funny–I can’t stand when they are produced as serious plays.
It helps to know a bit about the political scene in England at the time, but it’s not necessary at all for one’s enjoyment. When we used to see these done in summer stock, they would sometimes update a line or two to some current event reference that would bring down the house. Good times indeed. 
I recommend Anna Russell’s “How to Write Your Own Gilbert & Sullivan Opera.” I believe it’s on YouTube.
I know Pinafore, Pirates and Mikado nearly by heart, but for some reason the only other one I’ve really listened to is Trial by Jury, which is fun (The Judge’s Song: “So I fell in love with a rich attorney’s elderly, ugly daughter”). I really need to sit down and listen to rest of them.
The Canadian Broadcasting Company has versions of the [Canadian] Stratford Festival productions of MIKADO, IOLANTHE, and PIRATES that are wonderful, fun, bouncy, etc. One problem I’ve found is that some productions are too staid, too static. I love the Joseph Papp PIRATES (with Kevin Klein et al) and wish it were on DVD (as others have mentioned.) My favorite is MIKADO, with the patter song “I’ve Got a Little List” and the amazing “Here’s a Howdy-Do.”
If you had caught me prior to 1984, I could have obliged… my parents had a set of every D’Oiley Carte version from some time in the 1930s, I can still sing My Name Is John Wellington Wells 
Unfortunately the house burned and they lost all their records 
My absolute favorite is The Mikado, followed by Pirates of Penzance. Trite as hell, I know but there you go =)
Ha, I knew I saw it somewhere recently - on EMusic
Actually, the original Papp production with Patricia Routledge was videotaped, and it is linked on the IMDB page for the film to Amazon. This is very annoying, because I want the film. But I rented the “Broadway Archives” DVD. It looks like they just pulled a 3/4" dub copy off the shelf instead of going back to the original 2" master tapes. There are credits for a multichannel recording, but this is in mono and has noticeable SMPTE time code noise.
Yeah, gaffa, I made the mistake of purchasing that tape, hopeful that it would be fun. It’s a horrible taping, with poor sound reproduction (static) and grainy photography. I do not suggest it for anyone, and certainly not a newcomer to the G&S ouevre.
A) The best patter song (IMO) is either the “madness” song from Ruddigore (“generally rapid unitelligible patter/is very seldom heard and if it is, it doesn’t matter” sung at a billion notes per second) or the “Heavy Dragoon” one from Yeoman of the Guard (Which as Asimov said in hsi G&S guide, is the annotator’s nightmare.)*.
B) My favorite, outside of the “big 3” is Ruddigore**.
C) My favorite opening number is from Trial By Jury (“Edwin, sued by Anglina, shortly will appear”)
*It’s public domain, so…lyrics:
If you want a receipt for that popular mystery,
Known to the world as a Heavy Dragoon,
Take all the remarkable people in history,
Rattle them off to a popular tune!
The pluck of LORD NELSON on board of the VICTORY -
Genius of BISMARCK devising a plan;
The humour of FIELDING (which sounds contradictory) -
Coolness of PAGET about to trepan -
The grace of MOZART, that unparalleled musico -
Wit of MACAULAY, who wrote of QUEEN ANNE -
The pathos of PADDY, as rendered by BOUCICAULT -
Style of the BISHOP OF SODOR AND MAN -
The dash of a D’ORSAY, divested of quackery -
Narrative powers of DICKENS and THACKERAY -
VICTOR EMMANUEL - peak-haunting PEVERIL -
THOMAS AQUINAS, and DOCTOR SACHEVERELL -
TUPPER and TENNYSON - DANIEL DEFOE -
ANTHONY TROLLOPE and MISTER GUIZOT!
Take of these elements all that is fusible,
Melt 'em all down in a pipkin or crucible,
Set 'em to simmer and take off the scum,
And a Heavy Dragoon is the residuum!
If you want a receipt for this soldierlike paragon,
Get at the wealth of the CZAR (if you can) -
The family pride of a Spaniard from Arragon -
Force of MEPHISTO pronouncing a ban -
A smack of LORD WATERFORD, reckless and rollicky -
Swagger of RODERICK, heading his clan -
The keen penetration of PADDINGTON POLLAKY -
Grace of an Odalisque on a divan -
The genius strategic of CAESAR or HANNIBAL -
Skill of LORD WOLSELEY in thrashing a cannibal -
Flavour of HAMLET - the STRANGER, a touch of him -
Little of MANFRED (but not very much of him) -
Beadle of Burlington - RICHARDSON’S show -
MR. MICAWBER and MADAME TUSSAUD!
Take of these elements all that is fusible -
Melt 'em all down in a pipkin or crucible -
Set 'em to simmer and take off the scum,
And a Heavy Dragoon is the residuum!
Oh man, I hate it when they do that.
Gilbert was a master wordsmith. Other than two references, one of which was changed by Gilbert and the other has such a different meaning nowdays, I prefer not to hear his words messed with.
*Both from the “Little List” song in The Mikado.
Gilbert changed:
“People who chew peppermint and puff it in your face”
to the better
“People who smoke cigarettes and puff it in your face”
and someone else changed
“The nigger serenader and the others of his race”
to
“The banjo serenader (or entertainer) and the others of his race” (which doesn’t make sense, but won’t start riots, so…net plus, I think)
I’m surprised I’m the first to recommend Asimov’s Annotated Gilbert and Sullivan.
The thing I love most about G&S is that they found a way to make pointed political and social satire that was upbeat and positive.
Dare I recommend one of the best ways to get to know them is to get in touch with your local amateur theatre company or G&S society and get involved with their next production? To get to know it, there’s nothing like doing it…
Yes! This is her second most famous piece, after the “Ring.”
I’m a huge G&S fan, and I’m reluctant to name a favorite, they’re all masterpieces. But my most memorable performance was several years ago, in Long Beach, NY, I attended their annual performance of The Mikado . . . in Yiddish! :eek:
Nitpick–“Heavy Dragoon” is in Patience.
Round these parts folk still rave about the 1974 grade school production of Ruddigore, in which an 8th grade Dinsdale trod the boards as Sir Roderic Ruddigore.
- When the night wind howls…*
What fun!
Was a tad surprised - and quite pleased - at the extent to which all 3 of my kids, who generally have quite different tastes, enjoy G&S. As others have said, Pirates, Pinafore, and Mikado are pretty much required to have a basic G&S vocab. Of those 3, Mikado is probably my personal fave. So many hummable tunes. Then take it from there wherever you wish.
I’ve always wanted to see the HMS Pinafore after Sideshow Bob sang a bunch of their songs prior to attempting to kill Bart.
I know it’s not strictly on topic but I can’t resist recommending Tom Lehrer’s song The Elements. It’s sung to the tune of “I Am The Very Model of a Modern Major General” from Pirates of Penzance.
What’s a tyro?
BMW car from the '40s. 1200 cc engine, front wheel drive. Not a good seller. 
I thought it was a style of hat.