you say let me fill you in first when you want to provide information about something (example: I used to be best friends with this person, but we haven't talked for a very long time. He was always a very nice person, but didn't talk that much) before saying what you want to say.
let me set the scene for you first doesn't get used that often. it's less general. you say it when you want to describe a scene (example: we were in a restaurant, and it was very quiet because nobody was there)
there's other ways to say it, but these phrases don't get used often. Most of the time, if people want to provide background information, they will just start off saying it directly. these phrases will get used sometimes when strangers who are in a professional setting (like a job interview) are talking to each other.