I make it a point to read through the Bible every year. I start with Genesis and end with Revelation. What happens in the middle is completely random to me. A few things:
1) Even though I've read the whole book through several times, I learn something new every year. Things that seem strange at first make sense after you've read it a few times.
2) Sometimes it's not always easy. Certain books of the Old Testament in particular are hard to work through.
3) If possible, try not to view things through the eyes of an American in 2015. Things that might seem like random oddities to us made perfect sense to the original audience. Because we live in such a different culture, it can be hard to see how some of the Old Testament commands are relevant to us today. But, the reason God gave the Israelites the commands in the first place give us insight into His nature, and that's still relevant.
4) A lot of the things we view as peculiar in the Old Testament make a bit more sense when you read the New Testament. When you consider that Jesus was the fulfilment of the Law, it clarifies things. The burden of the Law was extremely heavy, and I think that was the point- to make it obvious that no one created could completely obey God's laws. Peter's vision where Jesus tells him not to call "unclean" what has been made clean wasn't about food. It was a declaration that God's plan of salvation was open to the Gentiles, as well as the physical descendants of Abraham.
5) In my opinion, the two books that really blow Christianity wide open are John and Romans. You could spend a year just studying those two books.
If you have any questions, feel free to PM me. I don't claim to know EVERYTHING, or even to be an expert, but I'll try to help as best I can.
You're probably more than smart enough to do it. Just acknowledge ahead of time sometimes it won't be easy going.