Beethoven Moonlight is tough in a sense that so many great pianists have played before, and we would probably have one or two favouite versions in our mind. You might get seriously benchmarked against Brendal, Gilels, Arrau, etc. Beethoven PS #5 in C minor Op 10 No 3 or #27 in E minor Op 90 may be easier.
It's technically less challenging to play Mozart, but if one has to make the Mozart sonata sound really Mozart, that's a lot effort. Nevertheless, Mozart K310 had also been played by many great pianists, too.
It's good fun to explore pieces, you'll learn a lot quickly: not necessarily that you will be able to master all of your shortlisted pieces, but hopefully you'd enjoy the process and experience.
Any way, so many classical sonatas to explore. Have you looked at Haydn and Schubert, too?
Good luck.