Starting with the Gospels is not a bad idea, but since they depend on the Old Testament, I recommend reading this easy to read summary of the whole Bible (OT included) so that you have a better idea of the significance of the NT. It says "Catholics" in the title, but its good for any denomination to read.
Dr. Bergsma has another great book that's also easy to read: Bible Basics for Catholics.
Genesis one is an establishing shot, while Genesis 2 telescopes into the Garden and Adam's liturgical roles.
This book explains it very well.
The way I started - that made Scriptures more accessible to me - was to begin reading one of the Gospels first.
If you are new to Scripture, begin with Mark.
Also, be S.M.A.R.T. about reading Scripture. Be specific in your goal. Make your resolution measurable, attainable, realistic, and be timely in enacting your resolutions.
If this is your first time actually spending time with Scriptures and reading through them, start with only two chapters a day. This is a small goal, and very attainable.
Once you get through Mark, I recommend simply moving on to Paul's Epistles (beginning with Romans), and repeating the process. After you get through Philemon, you should have a better understanding of how you read and process Scripture, and you can move on to reading Acts, Hebrews, and the remaining New Testament epistles.
Having a knowledge of the Old Testament is indispensable, of course, but for that you may need some guides to help you along. I recommend Bible Basics for Catholics by Dr. John Bergsma.