I would have to go this way:
Independence > House > NCR > Legion
If i could just pick one i would have to go in the independent way, and i would go with the Brotherhood of Steel as my begining of a real future for humany. But if for instance i could put put myself in that Post Apocaliptic world, like the The Courier or the Lone Wanderer, i would find a way to put myself in the head of the BoS, but just and only by non violent ways, i would have to change, or yet better, eliminate the "Codex", let new recruits join the brotherhood, but just people that is smart and strong enough to survive in this new world. Maybe i wouldn't have an army as big as the one the NCR has, but it would be enough to keep people away. Quality over quantity. Once all of this is done, and have enough firepower to defend ourselfs, i would kill every single raider and troblemaker that is one hundred yards near our main base/chapter, i would go myself, and other 5 Paladins to wipe out every single threath to the brotherhood, every single building and cave would be cleaned from anything that i would consider evil; by the words or by the guns... only by guns if it's evil, it doesn't matter, that will happen because i'm in there. It doesn't matter if it is a human, a ghoul, a supermutand, or any agressive folk that comes in our perimeter, this may take 2 years too far, in a real life time. Afther this is done we can make the rest of the people out there work in farms, but only volunteers (not part of the brotherhood, but they have a home, food, work and security), from and outside of the brotherhood, they wouldn't be protected by our elite army but by robots, some brotherhood knights and initiates and maybe some Paladins in Power Armor, yet the only serious threath to them are mutated animals, since every agressive human near is already dead.
Afther this is done i would send the brotherhood knights and scribes to search in every single building that may have pre war technology or schematics, while the paladins search for every single weapon out there, we don't want any citizen caŕrying guns and making a rebelion, weapons are prohibed by non-brotherhood members, we already gave them food, a work, clean wather, security, etc, they don't need guns, they can leave with their guns as long as they don't step BoS's land (Yeah, kind of tyrand, but this isn't a democracy, this is the future). Any serious crime would be punished by dead. And once our scouts became aware of the existence of the Big Mountain... that would be our fortress and, the last hope to humanity itself. Once that we kept control of Big Mt, the posibilities are endless to the brotherhood. We would have the best soldiers out there, having at least 900 Paladins in power armor, and diferent kinds of guns, being the best trained, armored, and equiped badasses "soldiers", with me as their leader, like that wasn't enought... That without counting the Knights witch are more. We would have armies of robots and cyborgs, we would improve our agriculture, and make our citizens live even better than the actual US (unless you're rich or something, but forget about capitalism or any other sort of government you know), you have to work, we are not the Followers of the Apocalipse who are going to here and there giving knowledge to everyone, they basically created The Legion even if that wasn's their intentions, just a bunch of optimist people. We would search knowledge and build elite schools, and military academies (all of this ouside Big Mt, that place is only and ONLY for the "Elite part of the brotherhood and scientists (BoS scribes, The Think Tank, Dr. Mobius)". I would try to search peace with the NCR, they are not so bad, just too ambitious and selfish, they are just living by the Pre-War tech, they don't look for a real future. But still, i want peace with them, and if i'm lucky and make some plans, i would try to abduct, just like they did with the Rangers. But if not it's ok, we can work together, just stay out of our land and resourses. And if some stubborn old politician want a piece of what the BoS is making with their own hands, all of the NCR's Army would be wiped out before a year. You can be sure of that. After that all of this is settled, we would have only progress, thinking only in the progress the Big Mountain has, we would make endless experiments of all sort, we would have factories near (not inside) the Big Mountain, i would make so much for the world... that is too much to say, i'm already tired of writing. But i can say that if any other group like The Enclave or The Legion is stupid enough like to mess with the BoS (they don't even know of the existence of the Big Mt LOL), their leaders will end up with a piece of steel in their asses, literally.