Selecting a POV is a pretty difficult thing in general, but having a branching CHYOA story adds a whole nother dimension of complexity. The nature of the decisions made in your story have an impact on which POV is most appropriate. There are actually four primary POVs in fiction, and I'll go through each of them.
First Person - This is generally regarded as the easiest perspective to write from, since you can get inside the protagonist's head and plainly state their emotions without it feeling clunky. You need to narrate in a certain tone, and by writing in first person, you can conflate the narrative voice with the protagonist's personality by simply writing as though the protagonist is relaying events (this isn't exclusive to first person, but much harder otherwise). That said, first person isn't necessarily, or at all, the best option. You are essentially required to describe things from the protagonist's point of view, so that if they perceive things in a different way to reality, you will struggle to communicate that to the reader without abruptly breaking the writing flow. In terms of choices, first person is best for when the choices in your story are all made by one character, but the reader is not exactly given control over them. The character makes plenty of decisions themselves, and choices are restricted based on their personality. The reader is less of a controller and more of an advisor who helps them out in certain situations. If you want your character to be distinct from the reader but highly relatable, then first person is your best bet.
Second Person - This is almost exclusively associated with choose-your-own type stories. Writing in second person directs all of your language toward making the reader feel like they're one with the protagonist. Choices feel like real decisions that affect the reader, personally, so it's perfect for game mode stories and others where the reader gets maximum influence over a single character. Immersion is basically inevitable in second person. Its biggest downside is, of course, that the protagonist will often be flat; you can't just tell the reader they think or feel certain ways and expect them to accept it. Saying, "Bobby is horny," is an obversation. Saying, "I am horny," is a proposition. Saying, "You are horny," is an assumption, and a rather confident one at that. If you want your protagonist to be a blank slate that the reader fills with their own personality, or if you want your reader to not only see the world through one character's eyes, but interact with it as them, then second person is for you.
Third Person Omniscient - The difference between 3rd POV Omniscient and 3rd POV Limited isn't as well known. In this variant, the narrator is not confined to a single character or group of characters, instead able to report on everything in a purely factual sense. Nothing needs to be hidden from the reader. Put simply, because third-person omniscient allows you to view the thoughts and motives of all characters, in an interactive sense, you're allowing your reader to play god. In a different manner, 3rd POV Omniscient is good if you have a cast of characters that follow different plots. You can easily flow between a variety of voices without abrupt changes in narration, essentially confining yourself to certain perspectives by way of what content you write about, rather than your word choice. If you're looking to maximise relatability in your characters, 3rd POV Omniscient certainly isn't ideal. However, if your story's decisions tend to be ones that none of the protagonists can actually influence, or if you're more interested in reporting and describing events than confronting the reader personally, this is the best choice.
Third Person Limited - In this one, you're using third person terminology, but you're deliberately using language that restricts you to one character, or multiple tightly-knit protagonists. This is by far the most common in the 'real' world of writing, because it means you can both explain how someone thinks or feels explicitly, and demonstrate their emotions physically. People aren't self-aware enough to honestly describe themselves as hysterical or pathetic, so you can do it for them. 3rd POV Limited is the home of the age-old advice: show, don't tell. In terms of choices, it's not actually particularly tied to any style I can think of - broadly speaking, if your choices are 'objective' to some extent but all apply to the same character, then it might be best to restrain your writing to that character. Also, if your story is closer to traditional and its choices are sparse, then it probably wants 3rd POV Limited, unless you think first person is better. If you're focused on striking a balance between emotional investment and explicit storytelling, and the nature of the branching points in your story don't heavily lean toward another option, then this might be the preferable option.
