This is a somewhat-canonical timeline of events as they are known in the Firefly 'verse. Years of birth are based off the ages of the actors who play the characters in question. The production year of the '03 Firefly Transport is inferred. Dates within the Unification War have been restricted to canonical events -- the more-detailed, non-canonical version of the Unification War was not.
Notes on Mal's age, for updating the timeline (via Leah: email@example.com):
was born on September 20, 2468. This is taken from the Serenity movie when the operative
is viewing his file. This date has significance in that September 20, 2002 is the day Firefly premiered, and September 20, 1968 is Firefly writer/producer Ben Edlund's date of birth.
2444 - Patience born
2449 - Adelei Niska born
2460 - Shepard Derrial Book born
2468 - Malcolm Reynolds born
2477 - Jayne Cobb born
2484 - Zoe Alleyne born
2486 - Hoban "Wash" Washburne born
2493 - Bridget/Saffron/Yolanda born
2495 - Simon Tam born
2497 - Kaywinnit Lee Frye born
2500 - River Tam born
2503 - The 'Aught-Three' redesign of the Firefly-class medium transport begins production. (Dubbed the 'aught-three' due to the year of its release.)
2506 - Interstellar Civil War, or the Unification War, begins
2511 - Unification War ends
2511 - "Yolanda" married to Durran Haymer
2512 - Malcolm Reynolds buys a used Firefly-class medium transport and begins to assemble a crew for the ship he has named Serenity.
2514 - Jayne Cobb pulls a job on Higgins Moon
2516 - Inara and Captain Reynolds enter into a business arrangement regarding the leasing of one of Serenity's shuttles.
2516 - Jayne Cobb leaves his employer of the time and defects to Serenity.
2517 - Serenity takes on Shepherd Book, Simon Tam and River Tam