Guns, Germs, and Steel (Jared Diamond) is a great "pre-history" book - he does talk about contact between cultures, so gets into actual history as well (ie, Spain and the Aztecs and Incas) -- but from a more cultural perspective. It covers all six inhabited continents, and how civilization developed in those areas - horticulture, animal husbandry, and so on. It's a good rebuttal of some of the "Manifest Destiny" theory that some follow about how Europe ended up dominating so much of the rest of the world's economy, politics, etc. This book is commonly read in Into to Anthro courses in colleges ... it's a bit meaty especially at first, but it's worth the read.
If you haven't read
John Adams, it's a good history of the colonial and Revolutionary era and early years of our democracy - obviously from Adams' perspective.
A good history of the Civil War is
The Killer Angels. IIRC, it's about Gettysburg. I'm NOT a war buff, I'm not into 'battle plans' etc. but it was very readable, I inhaled it in one afternoon because I couldn't put it down.
I have not read
A People's History, although it's on my list. I do think it's wise to look for histories which are well-researched and less biased, because it's true that sometimes there can be a very biased tone/approach/assumption in a book even though it's historically based.
A People's History covers history from a perspective seldom considered, that of the common people and working classes. Which is why it is on my list to read.

And also why I suggest
Guns, Germs, and Steel - if you read that, you'll be able to decode some of the assumptions you may run into in other history books. Just consider the differences between how a Crow Indian would describe the last two centuries of history, compared to how it's been described in most history texts in our schools, for instance.