How long are they supposed to be (time limits)?
You can probably play any sonata if you are able to learn the Mephisto Waltz...so why take these rather easy ones?

No, no, I like these two out of op.31 more than the tempest. Personally, I would do the 3rd. What are you looking for (in terms of difficulty, style, lenght)?
Other sonatas:
for the obscure guy: op.22/(op.54)
on the easy side: op.27 nr.1/ op.26/op.28
on the hard side: op.7/op.53/op.57/op.81a/ any of the last three
on the extremely hard side: op.101/op.106
So... these would be MY considerations. If I were you, I would either choose between op.109/op.110 for a really spiritual experience, or between op. 28, op. 7 and op. 81a.
Guess Waldstein and Appassionata are overdone, Hammerklavier - nah. Op.22 can be very interesting, but it is really a bit the traditional Beethoven.
Currently learning op. 101. That is a hard one, but sure one of his best,and rather short (around 20 minutes). If you consider it, make sure first to have a very close look at the fugato development of the finale and the second movement.