I've been thinking about this for quite some time, but being the indecisive oink that i am, i feel that i require a third (or more) opinion. Remember, this has to include any and all Independent or Co-Dependent other factions in New Vegas as this is for economic, military and cultural stability throughout the Mojave

Mr.house of course he will make of the mojave the best wastland in america he dont want money he dont want the power he just want a better world

I'll go with the Courier and an independent Vegas.

Vegas doesn't need anyone else infringing on their sovereignty. If the Legion takes over, they will massacre it's citizens indiscriminately and ravage all that remains of the city in order to "purify" it and make it part of their new world, if the NCR takes over, it will lead to inevitable violence as even with a good karma Courier, there remains a lot of mistrust for the NCR in the Mojave. House remaining in power would also be a benefit purely for Houses interests, as oppose to the good of the Mojave.

I always envisioned the ending, based on a good Karma Courier, acting as a wild card to defuse the situation, and deliver a message of hope to the Mojave.
I think in the best case scenario, a good Karma courier acts as a voice of reason and conscience, removing the threat from Vegas. He destroys the Legion ideologically, his lack of intervention leads Caesar to die from his tumour, thus proving that the God-King is not the son of Mars, but a man, before forcing the Legate to retreat at Hoover Dam, defeating him with doubt, thus destroying his image as the great warlord who has never lost a battle. People would never look at him the same way again. Without Caesar to hold it together, the lack of a centre on which to focus the Legion's strength, a leader in Lanius who is neither a tactful leader, nor entirely feared, or a suitable replacement the Legion collapses in on itself, warring for the remains of it's empire. From this, new societies will likely emerge, possibly reforming into a true society. Though people trained to know nothing but war and obedience their entire lives have very little options when there is no one to obey. It was the inevitable fate of the Legion.

The NCR is sent packing from the Mojave despite it's military might. In the end, it's campaign amounts to nothing. There are many in positions of power and respect in the NCR, such as Chief Hanlon, who are against the war in the game. Their doubt turns to protest against Kimball and the ineffectual General Oliver, who take a lot blame for the loss of both life and territory in the Mojave, as Kimball was the main force behind pushing the NCR forward. Kimball's popularity plummets, and he is likely either forced to resign or defeated by an opposing candidate in the next election. The NCR never return to retake the Mojave, with subsequent leaders recognising the losses caused by overextending their reach. Instead, they attempt to consolidate their own holdings instead, combating the corruption mentioned in the game (such as the Van Graffs). In time the NCR comes to form a strong (if not partially tenuous) relationship with Vegas. The city state provides electricity and fresh water for the Republic, in exchange for trade in a number of goods from the NCR and it's merchant houses, the pair enjoy a mutually beneficial relationship.

As for the Mojave itself, all the communities are brought together by the Courier, who has aided each of them at different points and is highly respected. Freeside, North and Westside are reconstituted as a part of Vegas proper, enjoying protection of the Securitrons, though the threat of the Fiends is largely diminished, and eventually halted all together. Towns like Primm and Novac retain their independence and flourish in a new, safer Wasteland, roads watched closely the massive Securitron force. The Ranger Unification Treaty is repealed, leading to the reformation of the Nevada Desert Rangers, under the watch of Vegas' ruling council. The council is made up of representatives from the communities, chosen by their people to ensure all of their voices are heard. The Boomers become a major arms trader, branching out from their home in Nellis as they begin to understand which outsiders are and aren't evil. The Great Khans leave the Mojave, causing a collapse in the drug trade fuelling the Fiends. The fiends are heavily damaged and missing any semblance of leadership, eventually been driven into the Hills. Vegas begins to work alongside communities like Jacobstown, allowing the mutant safe haven to grow as a beacon to all Super Mutants across the wasteland. The Brotherhood of Steel in the Mojave begin to operate on the surface freely again, harassing the locals for technology in resumption of their mission of "preserving humanity." However, out of respect for the Courier who aided them, or fear of the strength of independent Vegas, the Brotherhood restrain themselves from violence or open confrontation.

The Courier themselves, takes no part in the day to day ruling of the city. Instead, they allow Yes Man to oversee the council in their place. Instead, the Courier operates from obscurity, guiding from the background, dividing their time between the Mojave and their base in the Big Empty, discovering it's secrets and the ever continuing research of it's Think Tank. Slowly, they reintroduce technology from the Big Empty that may prove beneficial to humanity. With this, the quality of life in the Mojave improves vastly, and while this is not a true blissful happy ever after, life improves vastly, and the Mojave wasteland and it's citizens are given something more important than an emperor, or taxes. They are given hope by the Courier, and an opportunity to choose their own destiny.

Sorry for the long winded reply. I realise this isn't really what you asked for, but I had to explain my choice somehow.

I chose NCR to me as the best choice for recovery. To me they will eventually pull together their over stretched forces after winning the battle for Hoover Dam and defeating Legion once and for all. Once NCR brings their forces together they can focus on eliminating the raiders plaguing the Mohave and making the roads safe. Then they will be able to restart the economy and bring peace to New Vegas. Then the Mohave Wasteland and New Vegas will finally be at peace and become closer to how the world once was.
Any other option would in my opinion involve still warring factions who would still fight each other for dominance over the Wasteland. Indipendant New Vegas would still have to defend itself from enemies who would want to take it. Legions rule does not sound like a good deal and even if you did side with Legion what would happen after Ceaser died eventually? Infighting and Civil War most likely.
House would be the same issue with Independent Vegas as seen with the situation of the game, there will always be a outside threat looming in the distance. That is why I chose NCR