Bloodborne has a whole bunch of kooky characters to meet as you slash and maim your way through Yharnam, each one providing details about the overarching story and the different factions that are a part of it. For example, you have the Healing Church which is a group described as the direct cause of the plague in Old Yharnam and most of the events that take place throughout the game.
Which of the existing factions you actually join isn't that big of a deal in Bloodborne from a gameplay perspective, but fans have been discussing which ones they'd actually join should they ever find themselves trying to live out their days in Yharnam. The question was put to the Bloodborne subreddit by u/Chief_Horizon and as you can probably guess with this kind of prompt, responses were quite mixed.
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We'll start off with one of the more popular choices, that being The League and its charismatic, bucket wearing leader Valtr. While it's more of a jokey pick than anything else, u/A_Very_Sus_Bush likes the covenant for its simplicity, as simply going out and hunting beasts is its sole aim. However, u/TheBlackestOfKnights is quick to point out that Valtr's definition of "beast" is questionable and that the whole covenant feels a bit murdery as a result.
If you lived in Yharnam and were a skilled Hunter, which covenant would you join? from bloodborne
Another popular choice picked by an awful lot of people is the Vilebloods, which makes sense considering how they're kind of an underdog and no one really likes their rivals the Healing Church. Reasons why are pretty broad though, ranging from the mystery surrounding the blood of Queen Anallise to just wanting a big castle to muck around in. The only downside though, as u/Necro6162 points out, is that living there would be pretty chilly.
There're plenty of other choices and reasonings behind them, far too many to go through here, but one of the more wholesome answers comes from u/KanesaurusRex, who explains that they'd probably just go and chill out with Djura in Old Yharnam. He does seem a bit lonely on top of that tower all by himself.