If I'm preaching I would be looking at:
Genre - letter, myth, gospel, psalm etc
Language- I have a working knowledge of Koine Greek and Latin but my Hebrew is nonexistent. Two of my churches like the 17th century King James Version of the bible but there are better translations out there.
Translations - a good starting point is often to read the passage in a number of translations. Why did the translator use the words they have? What assumptions underlie particular translations ?
Who wrote it and why? Where has there is there been editing and rewriting particularly on the OT.
What do the church fathers, recent commentaries and older commentaries have to say about the passage? Is there something bang up to date that I can find that has some interesting new ideas about it?
Can I read it from the margins? What do third world or feminist or queer or disabled theologians say about it?
What do I need to understand about the culture of the day to help make sense of the passage?
What did I say about the passage the last time I preached on it? As I'm C of E we are on a three year cycle and if I'm really stuck I see what I did 3,6,9,12 years ago to see how what was happening then affected how I preached it.
It's a lot of work.