How about telling F3 from the start instead of continuing from where the last game took of?
How about being the son of someone who survived the nukes. Playing as the father, as some kind of intro of gameplay in the beginning. What happened just before the nukes hit and how your father survived. Then it switches to current time. Your father is laying on his death bed or something like that. Telling you what has happened.
In F2 you play the first heros (F1) descendant, in this game you could play as the father of the first hero (F1). A theme you could say.
From there on you will meet BOS, the enclave and other of those kind of groups, when they are young(er) and you can get to know them better and their purposes. There are also room for other factions that can be found in F1 and F2, as the zealots.
How about giving an explanation about tribes? How about getting to know how the war
really started and so on. The crisis about this time, what was peoples standpoint to the first mutants, and what has the mutants to tell you (FEV)?
I may be very well be wrong about times and years, as I has not THAT much knowledge of the fallout world. Correct if I am wrong. But what do you think of all this?