I would suggest you visit a bookstore, or a library, and get a commentary, or study book on one of the Gospels. Start there. The book of John is especially good, as it deals with how believers should love one another. Commentaries are good, in that you are getting someone else's (usually a true Bible scholar) understanding, and you can compare it with what YOU understand when you read it.
If you run into questions that pertain to the Old Law, or something that happened in the OT, then you can research that tangent, then come back to the Gospels.... those books are the TRUE good news about Jesus, and who He was. From there you can go into the letters to the early churches, or read the Acts of the apostles. All of that helps to explain, and build on the first 4 books... the good news.
While the OT is good and valuable to read, and has all the background about WHY Jesus came, and why it was necessary, the NT is what impacts our lives, and our understanding the most.