Knecht's work is a pedagogical staple of the late 18th century, focusing on clear thematic development. Its distinctive feature is the pedagogical clarity with which it presents standard variation techniques.
Emphasis should be placed on maintaining strict rhythmic pulse across varying note densities.
Comparable difficulty and character — good candidates for what to learn next.
12 Variations on a Theme in C major is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 5.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of 12 Variations on a Theme in C major lasts about 4 minutes.
12 Variations on a Theme in C major is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include 18 German Dances and Esoccaises by Franz Schubert, 18 German Dances and Esoccaises, by Franz Schubert, 18 German Dances and Ecossaises by Franz Schubert — see the full similar-pieces list on this page.