You do not need to read M.C. Beaton's books in order. Although the writer's two series of books are about the same main characters, they are episodic and each contains a beginning, middle and end.
M.C. Beaton, whose real name is Marion Chesney, wrote two series of mystery novels: those about constable Hamish MacBeth and those about retired advertising executive Agatha Raisin. Although both series feature recurring characters in addition to the main characters, they are self-contained mysteries and each comes to a conclusion by the end of the book. As a result, the books can be read on their own or out of sequence.
However, the novels contain references to earlier plots and recurring characters, making it enjoyable for a fan to read them in order.