What songs should I play?

What Sonatinas? There are an extraordinary number of Sonatinas ranging from easy to very difficult. However, I would recommend trying Invention No. 1 by Bach (I learned this not too long after Fur Elise), By the Limpid Stream and/or Arabesque, both by Burgmuller, and Prelude in C Major also by Bach. You could also do Sonata, Op. 49, No 2, by Beethoven, and possibly Sonata K. 330 by Mozart