Choosing a ball for Mime Jr.? Compare the normal and shiny recommendations below with their reference sprites. “Best” here means a colour or theme match, not improved catch odds.
The community colour-match recommendations for Mime Jr. are Heal Ball, Dream Ball.
The community colour-match recommendations for shiny Mime Jr. are Heal Ball, Dream Ball, Friend Ball.
Choose the appearance you prefer from the listed options. Normal and shiny Mime Jr. can suit different balls; these are community suggestions, not a measured ranking.
Source: Legal Matching Pokéballs 2.1 by OracleLink. Community recommendations, not a per-game legality checker. Availability depends on the game, form and encounter.