If you're trying to read from the start and go through from Genesis to Revelation, that's probably going to end up boring you to tears. Genesis itself may not be so bad, Exodus tolerable. But about the time you reach Leviticus your eyes are going to glaze over.
Not saying you shouldn't, just that there are some real snooze fests when you start reading a book about ancient Israelite priestly codes of conduct, or reading long lists of geneological material, "So-and-so begat so-and-so, who begat so-and-so, who begat so-and-so...."
It's important, don't get me wrong.
When I recommend someone to reading the Bible, especially if it's their first time seriously attempting it, I usually suggest starting with one of the Gospels, I recommend Luke. A lot of people recommend John, but one will quickly notice that John is a really theologically dense text, and it's theologically dense right from the opening verse. With Luke I also recommend the Acts, the Acts is in a sense the sequel to Luke. Acts begins where Luke leaves off, as both are from the same author and addressed to the same person. After reading Luke and Acts, one of the Pauline epistles, Romans is awesome.
After Romans and you want to test the waters with some Old Testament, you can't go wrong with the Psalms. Each psalm is a lyrical poem (most were meant to be set to music, so basically the Psalms were Israel's hymn book) and they are vibrantly expressive of the experiences of being one of God's people. Many are songs of praise, many are songs of desperate prayer seeking refuge from one's enemies, they are songs of repentance, they are songs of hope, songs of lamentation. Some are even songs expressing a desire for violent revenge. They cover the human emotional map.
After that you could pretty much go anywhere. I'd recommend more of Paul's epistles, I'm partial to Ephesians and Galatians.
But I'd really suggest, if you're coming to the Bible seriously for the first time, go to one of the Gospels first. And again I'm really partial to Luke, and Luke also allows you to very smoothly transition into the Acts. Acts introduces you to Paul, and that is going to help get to know the guy who wrote most of the New Testament.
-CryptoLutheran