House: The Courier has no real freedom. House will give him orders. The Courier can choose to disobey and shape the Mojave as he or she wishes, but I doubt House would allow him or her the luxury of being able to walk into Vegas without getting shot at if he or she disobeyed him. He's the best chance for New Vegas, but not the best chance for the Mojave. He's chasing the dreams of the old world, and that's not something we need. He's okay, but not the best choice in my opinion.
NCR: The Courier, again, has no real freedom. However, the NCR does not technically employ the Courier, so the Courier does have some leash for shaping New Vegas. Not to mention that, due to the Courier's high status, he has pull in NCR regional politics in the Mojave, the Courier will be better off. The main issue here is that NCR is very imperialistic and again, like House, chases old world dreams of vast empires spanning the world. They provide stability, however, allowing the Courier to focus on other things. They also look more towards the region, rather than just New Vegas, as House does. Overall, best choice in my opinion, but still not ideal.
Yes Man/Independent: Great on paper, horrible in practice. Doesn't matter if the Courier has a giant Securitron army - he/she cannot be at all places at once. Inevitably, some places will get worse treatment than others, and the Mojave may remain generally lawless for years to come until the Courier can personally conduct campaigns to eradicate all the regional menaces that plague the area. Stability is something of a luxury that, again, only New Vegas and the richer towns will be able to afford. In addition, due to the instability of the region, trade will generally be stymied unless the Courier focuses all of his/her man... er... robot power on patrolling trade routes, in which case other areas will go neglected. The best bet here is for the Courier to unite all the Mojave factions so they can do his/her work for him/her and allow the Courier to focus on more important matters. However, not all the factions get along. They'll unite behind the Courier, not the Courier's ideals. Should the Courier and the Courier's companions die, so the Mojave dies with them. Worse than NCR or House, but better than Legion.
Caesar's/Lanius' Legion: Stability is a key factor here. The Legion is stable so long as a leadership figure lives. As the Courier is an outsider, he/she cannot inherit the position of Caesar after Caesar dies - at least, not without heavy bloodshed. Lanius is too much of a brute, and his policies would likely destroy the Legion from the inside-out, leaving the Mojave a lawless waste. As long as Caesar lives, the Courier would be able to shape most of the Mojave to his or her liking - so long as he or she was careful about pushing Legion around. As soon as Caesar dies, however, the Mojave dies with him. His Legion troops, conditioned to be loyal to him - not his ideals - would quickly devolve into a mess of squabbling tribes, and the Legion would shatter.
I think Legion/NCR fans are very interesting and fun to listen to, and I understand why they support the Legion/NCR, but this post is completely false, with made up, exaggerated "what ifs"
House IS your friend. For god's sakes, he is the reason why you survived at goodsprings, and I'm not going to spoil the ending.
You can have an opinion, but you must also realize that the other factions have their own claim, and reason why they can be somewhat good at holding the Mojave.
I do agree that the NCR doesn't appreciate the courier enough, and refers to him/her as a civilian when the Courier was the sole reason why they gained power in the Mojave in 2281.
You need to finish Lonesome Road and then see your outlook on all the other factions after looking at Ulysses' philosophies.