Is Fallout 4 reasonably self-contained, or are there important pieces of backstory that would be better understood by playing earlier titles in the series?
I think the main thing you need to take from the lore in my opinion is the war of 23 October 2077 - The day of the nuclear holocaust, and the resource wars between the US and China that led to it (China being often referred to as the "communist threat"). The theme of the game is that of a futuristic 1950's due to how the timeline of fallout diverges from real history after the second world war. Instead of microprocessors, the world chose to pursue nuclear research, hence the nuclear themed world (cars using nuclear fission and even drinks!).
You will not be lost at all if you did not play the previous games. Those of us who did play them all will get a little extra kick out of the game when we are faced with the references and the throwbacks to some of the older games. Having said all that... do not worry, you will enjoy the world of Fallout and if you get sucked in you can always visit the older titles at a later date if you wish (which I can highly recommend - but it is my biased opinion).
I played all Fallout series including beta-version of Fallout Van Buren which was to buggy to play but just interested to start.
In my humble opinion you can leave F1+F2+Tactics only for fans, not to play in 2019, you will be completely disappointed with graphics and after could wondering - why these games are so epic? But they were miracle in 1998, not now.
Fallout 3, Fallout New Vegas, Fallout 4 mainly use the same interface, system and style - there is no big connection story between these games, not even the same place but the same universe.
So you can start with any but everybody love New Vegas as the game with incredible possibilities of choices.
In F4 your character was frozen during all the years and starts just now to see the new world. There are no important characters from old games, nothing to deal with so it is completely other history. And also - both prevous games are FPS Action-RPG with quests, no any settlements construction possibilities.
Yes, you can dig out - what happen with BoS and where is Enclave. But if you didn't play other games you will not have this question. There are a little bit from previous series but really a little. For example in Fallout 3 you can meet little child Macready.