Every journey starts with a small step. So if you want to start with the U.S. Civil War, you can go ahead and start with the U.S. Civil War. That is the joy of history, each new thread you learn adds more richness to events before and after that you already know. And then when you read about something a second time, you'll learn even more.

Yes, the U.S. Civil War has a long pre-history. Any good survey of the war itself will spend a full 1 - 2 chapters on events entirely before the war to get you grounded. Later if you want, you can read entire books to learn more about the pre-war period.

For a first book, pick up Battle Cry of Freedom by James McPherson. A very readable couple hundred page introduction to the war. Also, looks like Professor Gallagher released a new overview a couple years ago called The American War: A History of the Civil War Era. I haven't read this one yet, but in general Professor Gallagher's speeches and writings are very entertaining. From there see if there is a specific general that interests you and pick-up a biography (avoid memoirs in the beginning, they can be hit or miss, and some hard to read - President Grant excluded). If you live near a battlefield, grab a book specific to that battle / campaign and then visit the battlefield. Visiting the landscape makes everything richer.