I recommend buying some scholarly commentaries and diving really deep on a few passages occasionally. I wouldn't do this for all of your Bible reading, just because of the sheer amount of information (you might get like a 500 page commentary on Mark, for example), but they're wonderful reference books for letting you know about the surrounding cultural context, references to other parts of the Bible, etc. The ones in this series and the related "Old Testament Library" series, as well as the "Feasting on the Gospels" commentaries were recommended to me for beginners to reading commentaries.
They're pretty expensive, but it's not too uncommon for e-book versions to go on sale for like $4 each.