My first introduction to the fallout universe was FO3 then New Vegas. As such I really don't know much about the history of the different factions.
So I was wondering if y'all could provide a bit of backstory for the factions(NCR,BOS...) as well as let me know if there is a definite "good" or "bad" group.
I have the first two games ordered so you don't have to go into huge detail.

One very important thing to remember is there are no good or bad factions.
Each faction is a varying shade of grey.

You can use the http://fallout.wikia.com/wiki/Fallout_Wiki to find out about factions and the universe in general. It should still be taken with a grain of salt though.

The NCR was once a town called Shady Sands. They came from Vault 15 along with other groups called the Khans, Vipers and Jackels. The Vault Dweller saved the leaders daughter Tandi from the Khans. Tandi became the leader of Shady sands and Shady Sands formed into the NCR. The NCR expanded to take over all of Southern Califoria by the time of Fallout 2. With Tandi still as president of the NCR by the time of Fallout 2, some 80 years after Fallout. She then continues to expand the NCR to all of California and into southern Oregon thanks to the Chosen One, the grandson of the Vault Dweller.

The Brotherhood of Steel was founded by Roger Maxson. He was second in command of an army unit stationed at Mariposa Military Base. The Guy in charge killed himself and Roger took over. He discovered Mariposa was testing FEV on humans. He didn't like what he found. So he and his men killed the researchers and scientists at Mariposa. They tried to tell the outside world what they had found and done. But a few days later the Great War happened. Roger and his men survived because Mariposa wasn't hit. Roger took his men and their families to Lost Hills. There they became the Brotherhood of Steel.

For 84 years they did trade with outsiders. They took advanced tech away from people because they believed that by doing so they would prevent another great war. Sometime after Fallout and Before Fallout 2 they had a debate about letting in wastelanders, much like Lyons ended up doing in Fallout 3. But the Elders said no to it and sent the minority on a mission to follow the remnants of the Master's Army East over the Rockies. So they built airships. The airships ran into a storm which some said would happen. Some of the minorty crahsed outside of Chicago and there they formed a new Brothehrood of Steel, one free to do as they wanted. Fans call them The Midwestern Brotherhood of Steel.