I like Penguin because Mario looks cute and it's better than the Frog and Ice Suit.
Ice Mario from Super Mario Galaxy is just a cool powerup that lets you skate on ice and magma!
Flying Mario has very awesome effects. I like the red things streaming out of Mario's hands, and you can stop mid-air. It's a shame it only appeared in one game (Super Mario Galaxy) and in a few levels. It has a swell black outfit, too.
Anyways, my favourite three Mario forms would probably be Fire Mario, Cloud Mario, and of course Propeller Mario (I use Propeller Toad more too as well).
My reasoning for Fire Mario would be because it is probably the most iconic and classic power-up. It gives me good memories of SMB, and is also still useful to this day. Cloud Mario was a fun power-up to use in SMG2. I also liked Cloud Mario's design as well! Propeller Mario was a very useful power as well (the greatest and funnest way to recover!).
I believe "Plumber's Lament" is the name of a disguise. In Super Mario RPG: Legend of the Seven Stars, Mario has to be disguised as a statue in order to infiltrate a castle and the statue sculpter named the Mario "statue" "Plumber's Lament" in order to convince the villain to bring the Mario "statue" into the castle.