The Burgmüller pieces are supposed to be technical exercises but at the same time fun. The title does say "Progressive". Whether this means anything we're making progress practicing everyday.
Here is a piece I haven't played for a while but started playing again during the summer. It's the Bourrée from the Bach Lute Suite #1 (BWV996). It's in "First Lessons in Bach" that many students would play. In fact, out of the 6 movements in the suite, it's the only one that has a piano arrangement. The rest of the suite ended up as guitar pieces. Despite the title "Lute Suite", the pieces are rarely performed on a lute which they were not intended. The other movement from Prelude, Allemande, Courante, etc. are mainly performed as guitar pieces. So the Bourree has become a common piano student performance piece.
I came across the Bach Lute Suites online a few years ago after listening to a performance of the Bourrée from Suite #1 and soon realized this was the only piece out of the whole set a pianist would play. My version isn't the first and probably not the last. After leaving it for a while would take a bit of practice to get comfortable with the awkward fingerings. It's very comforting every time I play the Bourrée.
The other piece my teacher recommended before the summer break was "Minuet in G" from the Bach Suite in Gm (BWV 822). The Minuet found in repertoire books is actually Minuet #3. Bach included 2 other Minuets (1 & 2) in the suite. The other 2 are copies of each other with the LH & RH parts switched around. Only #3 in the whole suite is in G major, the rest of the suite is in a minor key. Worked on the Minuet 1-3 during the summer and made a recording on a public piano.