First, the Factions, and then, some information that is more specifically pertinent to Starscream's character
PREDACONS
The Predacons were descended from a small group of Decepticons that survived at the end of the Great War. While most Decepticons were executed for war crimes, the Decepticon Razorclaw was not, and founded the Predacon faction from the few remaining Decepticons who were not killed. The Predacons, unlike the Decepticons, had no particular ideology, and instead existed as a kind of underclass in Cybertronian society, looked down upon and sometimes even abused by the Maximals. One Predacon chose to rename himself after Megatron, and began a rebellion with the intention of leaving the Predacons in what he believed to be their rightful place as the rulers of Cybertron (as his ancestors should have been). He stole an artifact called the Golden Disk (in reality the disk from the Voyager spacecraft) and opened a Transwarp gate to send himself back in time to prehistoric Earth, his intention being to use the information on the Disk to change Earth's history such that the Decepticons would come out the winners of the war, thus leaving his ancestors the ruling class of Cybertron.
MAXIMALS
The Maximals are the descendants of the Autobots. They are smaller in size than their Autobot counterparts, having downsized due to the lack of fuel on Cybertron; now, they are closer to human size. Philosophically, they are close to the Autobots, ostensibly believing in the freedom of all sentient beings, but in reality being quite isolationist, not to mention their oppression of the Predacons. Optimus Primal was the captain of a simple exploration ship harboring a dark secret which was diverted to intercept Megatron. This ship, too, fell through Megatron's portal, and the young and untested Maximal was left with a ragtag crew of misfits to attempt to stop the renegade.
RAMPAGE
In order to understand Starscream's place in the Beast Wars timeline, it is essential to devote some time to Rampage. Rampage was the dark secret harbored by the Axalon, a creature created as a Maximal attempt to replicate Starscream's immortal spark. This suggests that Starscream's spark was held by a Maximal science lab at some point, and experimented upon. Given that the only other time we see a "clone" being made from a spark, it involves a piece of Rampage's spark being cut away to provide power for Dinobot II... so it is not unreasonable to conjecture that this may well have been the method used to create Rampage: cutting away a shard of Starscream's spark, letting it grow into its own, and implanting it into a new shell. The truth, however, is unknown.
STARSCREAM HIMSELF
Starscream himself appeared in one episode of Beast Wars, his mutant, immortal Spark having fallen through the same rift in space-time which had brought the others to Earth. There, he attempted to take control of both the Predacon and Maximal forces, but was thwarted when Blackarachnia, a Predacon, betrayed him.
BEAST WARS STUFF
PREDACONS
The Predacons were descended from a small group of Decepticons that survived at the end of the Great War. While most Decepticons were executed for war crimes, the Decepticon Razorclaw was not, and founded the Predacon faction from the few remaining Decepticons who were not killed. The Predacons, unlike the Decepticons, had no particular ideology, and instead existed as a kind of underclass in Cybertronian society, looked down upon and sometimes even abused by the Maximals. One Predacon chose to rename himself after Megatron, and began a rebellion with the intention of leaving the Predacons in what he believed to be their rightful place as the rulers of Cybertron (as his ancestors should have been). He stole an artifact called the Golden Disk (in reality the disk from the Voyager spacecraft) and opened a Transwarp gate to send himself back in time to prehistoric Earth, his intention being to use the information on the Disk to change Earth's history such that the Decepticons would come out the winners of the war, thus leaving his ancestors the ruling class of Cybertron.
MAXIMALS
The Maximals are the descendants of the Autobots. They are smaller in size than their Autobot counterparts, having downsized due to the lack of fuel on Cybertron; now, they are closer to human size. Philosophically, they are close to the Autobots, ostensibly believing in the freedom of all sentient beings, but in reality being quite isolationist, not to mention their oppression of the Predacons.
Optimus Primal was the captain of a simple exploration ship harboring a dark secret which was diverted to intercept Megatron. This ship, too, fell through Megatron's portal, and the young and untested Maximal was left with a ragtag crew of misfits to attempt to stop the renegade.
RAMPAGE
In order to understand Starscream's place in the Beast Wars timeline, it is essential to devote some time to Rampage. Rampage was the dark secret harbored by the Axalon, a creature created as a Maximal attempt to replicate Starscream's immortal spark. This suggests that Starscream's spark was held by a Maximal science lab at some point, and experimented upon. Given that the only other time we see a "clone" being made from a spark, it involves a piece of Rampage's spark being cut away to provide power for Dinobot II... so it is not unreasonable to conjecture that this may well have been the method used to create Rampage: cutting away a shard of Starscream's spark, letting it grow into its own, and implanting it into a new shell. The truth, however, is unknown.
STARSCREAM HIMSELF
Starscream himself appeared in one episode of Beast Wars, his mutant, immortal Spark having fallen through the same rift in space-time which had brought the others to Earth. There, he attempted to take control of both the Predacon and Maximal forces, but was thwarted when Blackarachnia, a Predacon, betrayed him.