As far as where to start, I would say that depends greatly on your taste. I don't want to make assumptions BUT for general Adam fanatics, I would think they wouldn't want to start with Queen or Queen II. Those are very fantasy based lyrics ogres, etc. It would probably be hard to get into those even though musically they are wonderful. BUT White Queen from Queen II would be a track to hunt down specifically. The only known songs would be Keep Yourself Alive from I and Seven Seas of Rhye from II. Queen II is my favorite album from the band. IT's a concept album and pure Freddie.
Sheer Heart Attack is the first time they went for radio. It's a ton of short songs but all very eclectic songs. I wouldn't say poppy but definitely less "progressive rock". Well known songs are Killer Queen, Now I'm Here, and Stone Cold Crazy (metal song)...just as a note one reason I like Queen what other tribute concert could open with Metallica and close with Liza Minelli?
Personal fav though is In The Lap Of The Gods..Revisited - I was hoping they'd include it with QAL.
(Sorry I can't bring myself to use Queenbert)
A Night At The Opera is their most acclaimed album. It's their Sgt Pepper....production to the fore -everything including the kitchen sink thrown in. Of course Bo Rhap is on it...Also includes 39, Love of My Life, You're My Best Friend, and I'm In Love With My Car - Underated track: The Prophet's Song.
A Day At The Races is kind of Son of A Night At The Opera - mostly recorded at the same time as Opera - includes Somebody To Love and Tie Your Mother Down - but some WONDERFUL deep cuts - Teo Toriatte (ballad to their Japanese fans), You Take My Breath Way (HAUNTING) and Millionaire Waltz.
News of The World was a new era - Stripped down and much more straight ahead rock - We Will Rock You/We Are The Champions/Spread Your Wings. Best track is It's Late - a great rocker with awesome vocals. Also a nice bluesy piano ballad by Freddie called My Melancholy Blues.
Jazz is a well liked album even if it's nothing groundbreaking - Fat Bottomed Girls/Bicycle race/Don't Stop Me Now are the known songs. Jealousy is a great piano ballad, Dead On Time a metal excursion, while Leaving Home Ain't Easy a great Brian sung ballad.
The Game - Pure attempt at pop rock with Crazy Little Thing/Another One Bites The Dust/Dragon Attack/Save Me (I don't know why they aren't having Adam tackle this one - one of my favs and he would do well with it.) Also includes the fine power pop of Need Your Loving Tonight, Piano ballad of Play The Game, and Brian's haunting Sail Away Sweet Sister.
Flash Gordon - music soundtrack - I love it, it's cheesy and it's very niche. Probably last on your list
Hot Space - The dreaded album among Queen fans when Queen attempted disco/dance music - Adam would probably like it...Under Pressure the best known. Staying Power is a good one, Dancer, Life Is Real (the song in Moscow).
The Works - the attempt to be a rock band again but turns out to be more of a pop album - Radio Ga Ga, Break Free. Highlight though undoubtedly is It's A Hard Life.
A Kind Of Magic - Hit or miss, mostly because it's a soundtrack - kinda. Who Wants To Live Forever, A Kind Of Magic are here. One Vision and Princes of the Universe great tracks.
The Miracle - Not highly rated by hardcore fans but I think it was a step back in the right direction - I Want It All is from here. But the best track is undoubtedly Was It All Worth It. Other highlights are Breakthru (would like to see Adam try this one) and The Miracle.
Innuendo - One of my favs - Show Must Go On/Days Of Our Lives are the known ones. Kind of a best of retrospective of the band. Some great progresssive Rock in Innuendo (REALLY wish they'd do this one), some gospel in All God's People, and a HAUNTING vocal in Don't Try So Hard. Also a fun track in I Can't Live With You (although a better version is found on the compilation Queen Rocks)
Made In Heaven - heartbreaking. Freddie's last tracks and some rerecorded solo tracks. Made In Heaven and I Was Born To Love You are from Freddie's solo career., Heaven For Everyone from Roger, Too Much Love Will Kill You from Brian's. Mother Love is Freddie's last recorded track, A Winter's Tale is his last written track. Let Me Live is a great gospelly track. Top notch.
QPR Cosmos Rocks - More Paul Rodgers dominated and far less campy. Not extremely well received but there are some gems. Roger's Small and Say It's Not True and Brian's Some Things That Glitter (Adam would do well with it I think)
To sum up? I think your best 4 choices are A Night At The Opera, The Game, Innuendo and Made In Heaven.
If anyone really wants to read it, I could sum up their various solo careers as well but I've probably written far more than will be read by most anyways
Personal fav though is In The Lap Of The Gods..Revisited - I was hoping they'd include it with QAL. 
(Sorry I can't bring myself to use Queenbert)
