These are only a few suggestions, feel free to choose your own!
SCENES
IOLANTHE
Strephon - scene after Good morrow, good mother (half a fairy)
Fairy Queen - scene before Foolish fay (manly beauty)
Mountararat / Tolloler - scene before Though p'raps I may incur your blame (sacred ties of friendship)
Lord Chancellor - scene before 'My lord, a suppliant at your feet I kneel' (victory, victory)
MIKADO
Katisha / Ko-Ko - scene before & after Titwillow (did he really die of love?)
Yum-Yum / Nanki-Poo - scene before Were you not to Ko-Ko plighted (if it were not for the law)
RUDDIGORE
Robin / Sir Roderick - scene after When the night wind howls (ghosts torture)
PIRATES
Ruth / Frederick - scene before Oh! false one, you have deceiv'd me
Pirate King / Major General - scene after Major General's song (orphan/often)
PINAFORE
Josephine / Ralph - scene before Refrain, audacious tar
YEOMEN
Jack Point / Lieutenant - scene after I've jibe and joke (cook's brain pan / overwound clock)
PRINCESS IDA
Lady Blanche - scene after Towards the Empyrean heights (list of punishments)
SONGS
TRIAL
Tenor solo - Oh, gentlemen, listen, I pray
Patter - When I, good friends, was called to the Bar
SORCEROR
Sop solo - Oh, happy young heart
Alto/bass duet - Welcome joy, adieu to sadness
Patter - My name is John Wellington Wells
HMS PINAFORE
Alto solo - I'm called Little Buttercup
Dramatic scene & soprano solo - The hours creep on apace
Patter - When I was a lad
Tenor/bari/bass trio - A British tar
Sop/bari/bari trio - Never mind the why and wherefore
Bari/bass duet - Kind captain, I've important information
PIRATES
Bari solo - Oh, better far to live and die ...I am a pirate king!
Sop solo - Poor wandering one
Patter - I am the very model of a modern Major-General
Bass solo - When a felon's not engaged
PATIENCE
Comic scene & bari solo - Am I alone and unobserved?
Bari solo - A magnet hung in a hardware shop
Tenor/bari/bass trio - It's clear that mediaeval art
IOLANTHE
Patter - Nightmare song (Love, unrequited... When you're lying awake)
Tenor/bari/bari trio - If you go in
Dramatic scene & mezzo solo - My Lord, a suppliant at your feet... He loves!
PRINCESS IDA
Sop solo - A lady fair, of lineage high
MIKADO
Patter - Little list song (As some day it may happen)
Sop/mezzo/mezzo trio - Three little maids from school
SATB madrigal quartet - Brightly dawns our wedding day
Alto solo - Alone, and yet alive... Hearts do not break
Sop solo - The sun whose rays are all ablaze
Bari/bari/bass trio - I am so proud
RUDDIGORE
Mad scene & alto solo - Cheerily carols the lark
Bari solo - When the night wind howls
Bari solo - Oh, why am I moody and sad?
SATB madrigal quartet - When the buds are blossoming
YEOMEN
Bari solo - I have a song to sing, O!
Mezzo solo - Were I thy bride
Alto/bass duet - Rapture, rapture
GONDOLIERS
Tenor solo - Take a pair of sparkling eyes
Mezzo solo - When a merry maiden marries
GRAND DUKE
Bari solo - Sausage roll song (By the mystic regulation)
Sop solo - How would I play this part
Bari solo - Roulette song (Take my advice - when deep in debt)