I remember learning it as a student in my 6th year (in Spain, where the grades are different from the British grading). I think it took me about two weeks to learn the notes decently, and probably two more weeks to get it up to performance level (interpretation, cleaning a couple of messy spots like those fast RH notes at the end).
I think it was the easiest piece I played that year. It's probably on the bottom three for difficulty among Chopin nocturnes, so... Fantaisie Impromptu, though, is a whole different story. I haven't learned it, but I'm sure it would take many weeks to get it half decent. The level is way different : gotta have very flexible fingers for the fast notes, gotta have a good brain to split LH and RH rythms, and stamina to play up to speed to the end. I definitely would go for the Nocturne, and after a couple of years of lessons, do the Impromptu.