I think that Beethoven wrote the most substantial variations of the "classical" period.
I maybe don't think the Diabllei/Eroica variations. Considering that there will be other players there. I don't think that your teacher would let you play for half an hour!

A possibility could be the 32 Variations in C Minor WoO 80. A great piece. It lasts around 12 minutes.
Another choice could be the variations op.76. Much shorter at around a 5 minute performance time. These are excellent variations though.
You could go through the other WoO variations, (they are on this website.)
Have you looked at Haydn? The F minor variations are also wonderful.
Have a look at some Mozart too. I think, however, that these would not be substantial enough.
Would you class Schubert as a classical composer? I would class him as in the same period as Beethoven, so if you say he is "classical" then I say Schubert is "classical" too.
He wrote a wonderful set of variations, (I think 10) in F. These are D. 176 I think.
He also wrote another set. D. 576
These are wonderful pieces.

Good luck choosing. Keep me informed!
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