By Beethoven I really like Sonata n.26 Les Adieux

is so various...
third movement (Rondò) of Patetique Sonata
If it's about the must-know pieces (also not piano music)I'd suggest:
1- At least one of his Sonatas (if possible avoid the easiest ones)
2- His sinfonias, the 5th,6th, 9th
3- His string quartet (are very important to understand the evolution of ensamble music) they tend to be very innovative if compared with Haydn or Mozart's ones.
4- Piano concertos are considerate as a turn ahead into modern piano concertos patterns (I'd suggest the third, that I would really like to try

if you'd like listen the third mvt)
5- violin sonatas are very beautiful