I really can't grasp the fascination with Fallout and New Vegas.
The setting in general is just a boring post apocalypse nr. 32452, with the only real distinguishing features being the bulky tech that isn't at all cool (no, not even power armor, it just looks like a walking soviet radiator). Also the kitschy 50's aesthetic combined with corporatist American authoritarianism of the past is a cool idea, but it can't carry the whole thing and gets old, especially when later installments start treating it at face value as epic cool art style and a descent into silly shit. I'd argue NV does some of this with the cartoonish ghoul rocket or that entire DLC set in a science park, or, when it comes to the silliness, the concepts behind the Khans or the Kings (or the entire Caesars Legion). Not to mention the burger-centrism of never showing the rest of the world. A good fictional setting actually makes you have some sort of attachment to the world, caring about how each region could develop and change, wanting to create a headcannon around smaller aspects never mentioned by the media piece and so on, but FO just makes me feel apathetic about it all.
And now specifically about NV - it is incredibly overrated, more so than Witcher 3 tbh. I don't understand why there is this internet culture of "which shitty / boring / underdeveloped faction best" debates. But I get ahead of myself. Let's talk about the general game before all that. In short, it is above average, but not special. Combat is... okay I guess. I don't really like it, but I know that there are enough FO3 fans that like that game specifically for gameplay only, so maybe its just me being subjective. The visuals, even though I usually don't hate on this, look fucking terrible. Like frickin' KotoR's looked better than this. I get that it is mainly because it is a desert and all, but even visually distinct stuff like different DLC zones etc look awful. But let's ignore that, as it is the story that we truly care about here. And it is, in my opinion, really meh. The journey your character takes is probably the best part, but still, I saw way more competent examples of it. Issue I see is that you get too much of a special treatment in the game. You'll say that it is due to the chip, but the problem is that it is just so easy for you to get robbed of it, and there is no real reason the faction leaders should trust me. House is extremely influential in Vegas. Surely it would be smarter to hire a yesman (pardon the joke) and just kill the courier. Similarly is with Caesar (with whom the only interaction you'll most often have is meeting him once, accepting his task, betraying him and then getting a pat on the back because the guy is too lazy to double check if you crossed him. Not to mention that to anyone else in the Legion you should be just another profligate. It is only the NCR that seem actually well developed in this regard, as you'll start with them as a free-lance grunt that eventually gets their trust to do more important tasks. But again, perhaps this is just my nitpick, so let's go into the main thing that spawns these discussions: the factions.
Pretty much all of the factions are completely forgettable. Legion is just a fucking joke. There are no redeeming qualities apart from "hey, maybe the merchant is slightly safer under us". Their entire system will collapse the moment Caesar dies and I just can't take them as a real threat, especially knowing that they are also luddites that hate advanced tech. NCR are better, but for a game that allegedly has such interesting factions, are just so basic. They are just a normie modern democracy that is expanding into a frontier, along with all the issues that arise from that. They could be way cooler if, say, we got to see their internal workings, perhaps see a faction that wants increased power for the frontier lands, perhaps some class conflict between the newly forming elites of the nation and the proletariat, or perhaps some sort of increase in authoritarian army control in order to keep control of an increasingly spread out country. However there is none of that. All we get is "these darn NCR be infringing our freedumz". House is probably the only standout faction, as he carries an interesting backstory, is generally charismatic and has a solid plan that is more than just conquer the other factions, but to instead become a power player that would become invaluable to NCR. Yesman is an interesting concept - uniting all the lesser regional players into an independent power, however the problem then becomes these smaller factions. Boomers just seem stupid - wasting wast amounts of invaluable ammunition just to isolate themselves, but generally are just another settlement with nothing more. The Kings are for the most part just a gang that just want to take care of their little neighborhood. And the Brotherhood are just people characterized by the fact that they have all the old tech. In the end this Vegas coalition ends up looking like a bunch of ragtag randoms without a coherent goal. Now, all of this that I said about the factions doesn't make the conflict boring, but it isn't that interesting either. Boil it all down and you get a choice of either: everyone suffers horribly / the region becomes the newest frontier of an expansionist republic / the region becomes an independent technological and technocratic powerhouse / the region becomes independent and does whatever you want to imagine. It's not really that engaging of a conflict, is it?
In the end I guess the main reason this NV fascination slightly pisses me off is because of all the other great RPG's with far more interesting conflicts that get ignored. Just of the top of my head, Dragon Age: Origins and Tyranny have far more interesting faction conflicts. I kinda wonder if this is because of the fact that Fallout is more accessible due to it functioning like an FPS. But then again, even Witcher 3 is more interesting with the who wins the war decision, but I rarely if ever see that part discussed. So again, I really don't get the fascination with Fallout specifically.
And to answer OP, House is the best choice