Choosing a ball for Mr. Mime? 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 Mr. Mime are Heal Ball, Dream Ball, Premier Ball.
The community colour-match recommendations for shiny Mr. Mime are Nest Ball, Friend Ball.
Choose the appearance you prefer from the listed options. Normal and shiny Mr. Mime 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.