First of all, I'd like to provide the disclaimer that [most] of us here are not teachers (and the few that are certainly have not worked specifically with you) and would like to suggest that you maybe save up a little money for a few lessons with a qualified teacher that could help determine both where you are now and a path that you could take in self-study for a few years.
Hanon and Czerny (and any other) exercises can be great, but I don't know that I'd recommend trying them without a teacher's instruction to make sure that you're doing them right and not practicing with poor technique. If you've built a solid foundation over several years' study, then you might be alright. Always practicing your 24 scales, arpeggios, and their inversions, however, is rarely a bad thing (use proper fingerings!).
As for repertoire, did you like the Bach that you played? If so, great! JS Bach is probably the single most valuable composer to familiarize with in improving at the keyboard (touch, articulation, fingering, dynamics, polyphonic playing). First Lessons in Bach
is a two-book series (Schirmer does have one book that merges the two) - did you play through both books (teachers commonly recommend completing at least all of the minuets before possibly moving on)? The next logical progression for Bach are his 18 little prelude and fugues, two-part inventions, and sinfonias.
I wouldn't be doing my job if I didn't suggest a varied and balanced diet of all kinds of pieces from different musical eras (Baroque, Classical, Romantic, and Twentieth-Century). For this reason, repertoire collection series are great. Succeeding With the Masters (editor Helen Marlais) is well-reviewed by teachers for just this purpose (see more suggestions here: http://www.pianoworld.com/forum/ubb...collection%20for%20leve.html#Post2014409
edit: I'm assuming you're talking about Beethoven's Moonlight Sonata mvt. 3. While not his most difficult sonata, it's also not his most approachable and it would be difficult to learn on one's own with but just a few years experience. The good thing is Beethoven wrote 34 other multi-movement sonatas (or 31 depending on if you're old-school) as well as a list of sonatinas and many
other beautiful works that may be more approachable (graded list of Beethoven sonatas: http://www.pianoworld.com/forum/ubbthreads.php/topics/503537/3.html#Post1930944