Bach is always good! I'd suggest maybe trying the Anna Magdalena notebook if you're really a beginner. I don't want to sound condescending, but the two-part inventions are trickier than they might seem, more so if you want them to sound musical and polished! Bach always takes more work than it would seem. I would recommend practicing all of the scales, both major and all groups of minor scales (natural, harmonic, and melodic). Every pianist should learn the scales and fingerings for them and such. What you should focus on is a proper balance of things you need and things you want. Learn a piece or chart that you want to learn, but make you sure you balance it out with about 60% more of stuff you need. Not only does this provide goals for you (being willing to work through the stuff you need to do in order to reward yourself with stuff you like) but it also provides something to look forward to before every practice session. Practice slowly when learning your music, and even after you've "mastered" it, go slowly back over all of the sections for accuracy. Once you learn all of your theory and are technically proficient enough to play a large portion of the standard piano rep, you're more able to put the stuff you need on the back burner and actually play what you want for 90% of the time. Just so you know, this takes years of dedication. But it's easily achievable for anyone with the focus and desire. So, get at it! :)
Now, I know this thread is about rep, but I felt like I should say something. :P I don't want to step on your teacher's toes, if you have one.
Good rep ideas:
Mozart K1-K5, or if you're looking for something a little tougher, Haydn has some wonderful piano sonatas that are technically achievable. Clementi and Kuhlau have some fun stuff as well! You might take a look at some of their sonatinas.
If you want something more romantic, some of the Chopin mazurkas are do-able, though expressively, they're an enormous challenge. Stephen Heller wrote some fine piano etudes as well, you might check some of those out.
Anyways, I think this is quite enough to get started with, so have at it and good luck! ;)