I can vouch for the Stillwell's one : Mathematics and Its History, and here's why:
unlike most math history books which are, well, focused on the history alone,
Stillwell's focus on the math.
That is, it's not about the mathematicians, but about the mathematics.
Each chapter deals with a math topic
(be it pythagorean triples, analytic geometry, etc)
and it even has exercises to help you get an idea on what the main involved ideas are.
each chapter has a supplement showcasing one or two biographies about the main mathematicians involved on the chapter's subject
But the real feature, again, it's that the book is structured focusing on the mathematics history, not the mathematicians history (hence its title)
There's also an oldie but goodie:
2 volume set Eves' Great Moments in Mathematics , part of the Dolciani Mathematical Expositions series
vol1 : before 1650
vol2 : after 1650
here each chapter is devoted to help you know about a specific mathematical breakthrough and why it's important on the mathematics development
This one starts talking about the Ishango Bone, which is dated around 10 tousand years ago, given you want to go far back as possible