Between 1931 and 1972, Georges Simenon published 75 novels and 28 short stories featuring Inspector Maigret. The following list is entirely subjective and includes only my personal preferences:
The Fayard Ciycle (1931 – 1934): The Carter of ‘La Providence’ (Inspector Maigret # 4); A Crime in Holland (Inspector Maigret # 7); A Man’s Head (Inspector Maigret # 9); The Saint-Fiacre Affair (Inspector Maigret # 13); The Flemish House (Inspector Maigret # 14); Liberty Bar (Inspector Maigret # 17).
The Gallimard Cycle (1942 – 1944): Cécile is Dead (Inspector Maigret # 20); The Cellars of the Majestic (Inspector Maigret # 21); Signed, Picpus (Inspector Maigret # 23).
The Presses de la Cité Cycle: a) The United States and Canada Period (1945 – 1955) Maigret’s Holiday (Inspector Maigret # 28); My Friend Maigret (Inspector Maigret # 31); Maigret at Picratt’s (Inspector Maigret # 36); Maigret’s Mistake (Inspector Maigret # 43); Maigret Goes to School (Inspector Maigret # 44).
The Presses de la Cité Cycle: b) The Return to Europe (1955 – 1963): Maigret`s Doubts (Inspector Maigret # 52); Maigret in Court (Inspector Maigret # 55); Maigret and the Old People (Inspector Maigret # 56); Maigret and the Saturday Caller (Inspector Maigret #59); Maigret Sets a Trap (Inspector Maigret # 60); Maigret’s Anger (Inspector Maigret #61).
The Presses de la Cité Cycle: c) The Last Part of the Saga (1964 – 1972) Maigret Defends Himself (Inspector Maigret #63); Maigret’s Patience (Inspector Maigret #64); Maigret Hesitates (Inspector Maigret #67); Maigret’s Childhood Friend (Inspector Maigret #69); Maigret’s Madwoman (Inspector Maigret #72).
Short stories: The Man in the Street (tr. Jean Stewart) in Maigretʻs Christmas: Nine Stories; and The Most Obstinate Customer in the World (tr. Jean Stewart) in Maigretʻs Christmas: Nine Stories.
However, if you just want to read one before making up your mind, I would suggest:
A Crime is Afoot 