From a first person pov I can make it very existential or light hearted. I can really manipulate the story as I see fit and there's probably going to be less plot holes.
From a third person point of view I can show how a non immortal may view an immortal, how they'd react and if their beliefs/faith would change or not.
I'm not sure where I want to start as well. How old is the immortal, is he relatively young (less than 100), has he been doing this for a while (Maybe a couple hundred) or is he very old (thousand years plus)? I feel like each would have different views of the meanings of life, how they portray themselves and what they want in their eternity.