Each version of the game "starts" at a different point in time.
Milieu 0: T4 covers the begining of the Imperium, or Year 0.
1000 - 1100: TravellerD20 (the d20 version of the game) takes place in the 100 years prior to Classic Traveller
1100 - 1116: Classic Traveller and Mongoose Traveller (1105) are set in this time frame, which includes the Fifth Frontier War (1107-1110) which involved the Zhodain, Sword Worlders, Imperium, and Vargr in the Spinwards Marches sector.
1116 - 1124: MegaTraveller covers this time frame which includes a time of turmoil where the Emperor has been assassinated and there is rebellion in the Imperium as nobles all over make power grabs.
1116 - 1124: GURPS Traveller shares this timeframe with MegaTraveller, but the assassination and rebellion never happened.
1200 - 1900: Traveller: The New Era takes place after 1200 and covers the aftermath of the rebellion and virus that wiped out almost all technology.
1902 - ????: T5 plays in thei area known as "The Galaxiad" and in the FAR FAR Future, though at this time there is no setting information published.
You can find this info on the
Traveller Wiki page about the different versions.
And you can find even more timeline info on
this wiki page and, if you have the GURPS Traveller core rulebook, there is like 50+ pages of info on events in the timeline.
The 1100-1116 era is one of the most popular mainly due to the fact that both Classic Traveller and Mongoose use it, and there was a ton of third party support for CT back in the day. Which is the same reason that the Spinward Marches (and now Trojan Reach) is the most used sector. It is on the "frontier", far enough from Capital to essentially be on it's own, and there is still plenty of exploring to do. However, if you want a setting with more turmoil, political intrigue, and general chaos, the 1116-1124 era of the Rebellion would be perfect.