If you talk to Jimmy, the guy in vault 13 in F2, he"ll say something about a rebellion in the vaults history. Now it seems that a concensus is forming about that F3 should be a prequil. I agree. So why not start just after the rebellion. You get summoned by one of the leaders and they ask you to find the BOS to purchase a computer. The BOS base (from F1) will exist but is abandoned (like vault 15 in F1) but isn't destroyed. You'll find some stuff but not the better weapons because the BOS, being tech police, wouldn't have left to many things luying around. Maybe some stims and a gun or two and some ammo. You'll also find a message on a holodisk for example that points you in a certain direction. After you find the BOS and asked them to help your vault with the computer, they tell you they had a rebellion as well. Some of them sell technology to the highest bidder and not to those that are deserving of it. They ask you to root the rebbels out. This way a lot of the towns that were in F1 could be implemented and you could see how they farred. A random encounter could involve Marcus and Jacob in which you point them in the direction of Broken Hills and even the Enclave who will ask you directions to the military base and in gratitude give you a suit of APA (the only way to get it).
JR
JR