I suggest you do get Fallout One and Two first. You can buy them pretty cheap and they come ready to play from GoG.com.
The story in Fallout 3 isn't connected to Fallout 2. But the main factions you encounter in the game are from the West Coast. The BoS are in Fallout and Fallout 2 and the Enclave are in Fallout 2. Since these factions can't be avoided and you are forced to side with BoS. Playing the Orginals will give you a better understanding of their history. It will also give you a much better understanding of the Fallout Universe, which Fallout 3 just fails at.
The game does explain the history of the Brotherhood, but I can't believe the number people that seem to miss all that and think the BoS formed in DC.
Also have you given any thought to Fallout New Vegas?
Also don't forget about Fallout Tactics