Choosing a viewpoint character can take a little thought, but some writers don't invest much time in the decision. They go with whatever seems right and sometimes that is enough, but here are a few thoughts that can be used either to decide on a viewpoint character or to uncover hidden problems that may exist with the choice.
The viewpoint character is the one (or more) character that becomes our window into the world. Obviously, this only applies to narratives with a limited narrator. It might be surprising what can change in a story when the story is told from the viewpoint (not to mention voice and opinions) of another person.
A well-chosen viewpoint character can offer insight and opinion on the world, whether that world is real or imaginary. A bland choice will live in the world, but have no thoughts about the world. Kind of ironic to see so much thought put into building a world, with no one giving that world much thought from within it. A good choice will not just see and describe the setting, but will let us know how they feel about what they see too. The same applies to people and events too.
Somewhat related to insight because it can offer an interesting and engaging portal into the world, voice can be tricky for many authors. I'm referring specifically to the character's voice. In several narrative modes, the character's voice bleeds through and colors the narration even outside of dialogue. Chuck Wendig's Blue Blazes is a good example of this. The story is third-person-limited, but the narrator sounds much like the main character due to the closeness of the narrative distance.
A viewpoint character may have secrets and information the writer wants to unveil. On the other hand, another character may have secrets and internal thoughts the writer wants to leave alone. I think Sherlock Holmes is a good example of this. Watson has opinions and his own interior, but Sherlock is left a little mysterious through the stories, and I think that makes the character much stronger. It is because his thoughts and decisions aren't laid out for us that we're so fascinated with understanding his mind.
Sympathy While sympathy is typically an attribute best left for a focal or main character rather than a viewpoint character, stories where the main character is unsympathetic for a good portion of the story might call for a viewpoint character that can draw sympathy. It can also be a good reason to make the main character a viewpoint character. The reader might need a better view of the character's interior (if one is offered) to fully sympathize with the character.
Writer of speculative fiction. Current work in progress is an untitled dark fantasy novella.