The benefits to reading "Outlander," or most book series in general, in order is that it is easier to understand the sequence of events that occur throughout the books, as they usually follow a chronological order. In the case of "Outlander," the books have many side stories in the form of novels about events that do not get full mention in the main books, so a reader could become lost if she did not read the connected books in order.
"Outlander" is a book series in which time travel is a main component of the story, so it is beneficial to understanding what is happening if one starts from the first book and follows onward. However, the official website for the author indicates that the books are engineered to be somewhat standalone, allowing new readers to jump into the series at any point. It still recommends reading the books in the order they were written, however.
The order starts with the eponymous book of the series, "Outlander," and carries on to "Dragonfly In Amber," "Voyager," "Drums of Autumn" and so on. Additionally, the book series about Lord John Grey is a part of the series but constructed in a way that allows them to be read separately without losing track of the story.