It has to be the chosen one.
There was purpose to what he was doing.
plus he was savage... literally.

I've only ever played 3, NV and of course 4 so I don't really have many characters to go off here.

On topic though, my favourite protagonist is always the Lone Wanderer because of the large amount of ease you can get personalising your characters story. Your given a solid background that makes sence and are then put into this world with two objectives. Find dad, find yourself. New Vegas doesn't do that for me, doesn't give us a fresh beginning as stated by Ulysess. We've always been a courier, not anything else.

4 has the issue of giving us what should be a rich backstory character without giving it to us.
I've only played the male character but from what we know he's a vet, and that's it. We don't know much else but on the contrary we should know.

Strong, from Fallout 4. I mean, yeah he's annoying, and yeah, he seems to have no purpose, and yeah his voice is grating in ways that defy the normal realms of what is tolerable, but, his line "the milk of human kindness" made sense to me. I've seen the movie Visitor Q, and the milk of human kindness is a theme which runs strong in the film. So, for my money it's Strong, because clearly he saw Takashi Miike's "Visitor Q" and was forever touched. Kudos to Strong. Peace.

Gota be the courier for me. I always loved the back story and I think FNV had some of the best character lines. Chosen one is a close second.

Sole Survivor. What a badass that guy is. Becomes Liam Neeson from Taken as soon as he wakes up from Cryogenic sleep to rescue his long lost son, only to find he now has to kill everyone on the face of the Earth to avenge his wife and save his son.

A close second would be the Lone Wanderer as he had the most personal story tbh. A naive teenager trying to find his Dad out in the harshest wasteland of all wastelands. Then he becomes a prophet and saves an entire wasteland of people by sacrificing his own life, only then to shrug it off a few weeks later and get back to fighting the Enclave. True hero.

The Vault Dweller. He was unlucky enough to be chosen to go out into the wasteland to find a water chip to save his vault, and along the way he saves a village from radscorpions, saves the future president of the NCR from raiders, travels into the bowls of a highly radioactive prewar base to recover a holotape, and destroys an army of mutants, on top of that, he finds the water chip and saves his vault. What a badass.

Plus he gets exiled and goes on to be the founder of the village of Arroyo, which in turn sets up the next game.

I think The Lone Wanderer is a pretty cool guy. Eh kills super mutants and doesnt afraid of anything.

I always liked Arcade Gannon, loved his back story and how we operated. I also liked dialogue, his intelligence when speaking really made him feel like a Followers researcher.

The Courier, he's much different than the rest of them. I like his story as well especially when you learn more from Ulysses in Lonesome Road. His journey is more unique than the others.