The TV series Firefly is first in consumption order, and is the basic location in the timeline for comparisons.
The comics Those Left Behind and Better Days are set between the TV series and the film. These answer some questions left open in both the TV series and movie, so could be read either between the two (chronological order) or after the movie (publication order).
The comic The Shepard's Tale covers a time period that extends from well before the start of Firefly to immediately before the movie. It contains a moderate spoiler for the movie, so is best read afterwards.
The movie Serenity is set some time after the TV series and those comics.
The comic Float Out is set shortly after the movie. It contains a significant spoiler from the movie, so should be read after it.
Creator Joss Whedon switched studios because Fox wasn't willing to let him do the movie. He created the comics to bridge the missing characters out. The comics are an important, although not vital, bridge.
Originally, the plot line was supposed to resolve over several seasons; when Fox canceled, Joss felt he needed to complete the primary enigma arcs (Reavers, River). The movie gave him the chance to do so.
The comics are also part of 'verse canon. They are primarily written by Joss' brother, with Joss' approval, exploring other areas of the story of Mal and associates.