As a general rule, when you’re writing in first person, it helps to know the narrator’s assumed reader or listener – that is, the fictional person or persons that your fictional speaker is speaking or writing to. Some first person narrators sound like a person telling their story to a single curious listener, at some comfortable time after the fact; some sound like they’re addressing a group; others use devices such as diary entries, voice recordings, letters, and the like to suggest that the story is being assembled or recorded for posterity in some fashion.
Some first-person voices are hallowed by tradition. There’s the reader-I-married-him voice of the Gothic novel, as exemplified by Charlotte Bronte’s eponymous narrator in Jane Eyre, and by the never-named heroine of Daphne DuMaurier’s Rebecca. There’s the noir-tinged private-eye voice of Dashiell Hammett’s Continental Op, or Raymond Chandler’s Philip Marlowe; and the confessional voice of the contemporary memoir.
The first person is not without its pitfalls, however. Some readers hold it in visceral disregard, often so intense that they simply will not read a story if they see that it’s written in the first person. Other readers react badly to dissonance between the perceived gender of the narrator and the perceived gender of the author. They are unable or unwilling to suspend their disbelief long enough to accept a male narrator in a story with a female by-line, or vice versa. And if you’re planning to kill off your viewpoint character in the end, first person will make it a hard sell.
(Well, you could always have the story being narrated by their ghost – it’s been done before – but it’s tricky to do that and still maintain suspense. Also, some portion of your readership will inevitably be disgruntled at what they perceive as an underhanded bit of literary trickery.)
As always, weigh what you want to accomplish by using the first person against what you may lose if you don’t pull it off as well as you’d like, or if some portion of your readership is put off by it, and make your choice accordingly.