Buster Brown is a vintage character piece reflecting the style of American parlor music of the early 20th century. It is heavily reliant on march-like rhythms and simple homophonic textures.
Ensuring a steady, driving march rhythm while keeping the left-hand alberti-bass patterns soft is key.
Comparable difficulty and character — good candidates for what to learn next.
Buster Brown is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 2.
You should be comfortable at Henle level 2 — meaning you can already play level 1–2 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 Buster Brown lasts about 3 minutes.
Buster Brown 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 Blumenwalzer by Léon Jessel, Bluin' the Blues by Henry Ragas, Bohemia by Joseph Francis Lamb — see the full similar-pieces list on this page.