Jesus, do NOT start with Zinn for your first approach to US history. That's like learning about German history from Mein Kampf.
Zinn is hugely biased, and his work is really only valuable when seen relative to mainstream history. He purposly focuses on antagonistic subjects and exaggerates both their impact and influence to make a point. It's like a combination of history and performance art. History is written to fit his agenda, not the other way around.
Give this a shot, for starters: http://www.amazon.com/America-Past-Present-Volume-Edition/dp/0321446623