I suggest Borg, Evolution of the Word which is the New Testament in his best guess of when the books were written. He begins each with an introduction to the culture of the time. Evolution of the Word: The New Testament in the Order the Books Were Written https://www.amazon.com/dp/B0070XFBI6/ref=cm_sw_r_apan_glt_D77ZVH4W8EH4K7YS2MD8
I also suggest you first do some reading about what Judaism was like at the time and what the Greco-Roman world was like at that time.
The Episcopal church (Im not Episcopalian) has a course which takes you through the basics over 4 years and encourages questions (at least my class did). Basically it is 1 seminary class per year. The name is Education for Ministry but I dont think that is a good name. There arent any expectations of becoming a minister, just of learning your path and understanding. The years are Old Test., New, church history, theology.