I'll admit the book list isn't terribly comprehensive (but I/other flairs haven't been bothered with updating a lot of it) - that being said, I'll put forward a couple special mentions:
Off the booklist:
Friday's Japan Emerging (2012) - great overview book, see review in booklist - it's good
Friday's Samurai, Warfare, and the State in Early Medieval Japan (2004) - another great book, review says it all and much more
Conlan's State of War (2003) - will admit, being primarily focused on the military, I'm biased towards that area, but it does cover a decent amount of political and religious/cultural influences on military doctrine which I find interesting
Otherwise,
(various editors) The Cambridge History of Japan (all 6 volumes) - Cambridge generally produces very good overviews of history (their illustrated history on China comes to mind) that work as a nice stepping stone going forward
Farris' Japan to 1600 (2009) - a dense book, probably more suited for when you have something specific in mind you'd like to know more about. Nevertheless, again a good starting point.
Farris' Japan's Medieval Population - Famine, Fertility, and Warfare in a Transformative Age (2009) - really nice sources and data that I personally think would be better appreciated after reading it through with knowledge already in the back of your head, as there is quite a bit of, again, dense analysis.
Bear in mind that there's not a lot of recommendations to be made for an overview of Japanese history so much as overviews of smaller periods (often with a certain perspective in mind - e.g. religion, culture, economy, military). Also, you'll find through cursory searches more books dealing with Imperial Japan and onwards, so that may make it a bit harder to find good, recent sources on Japanese history. So, I'd recommend maybe reading through one or two of these books, or going through the FAQ, or even finding short summaries online so you get a general understanding of history. After that, find an area you'd like to know more about (you can have many areas, but pick one first), and find books on those. This approach would (in my mind) be the best way to go about learning in any period over all history, as you'll find it very hard to condense many hundreds (if not thousands) of years with even more concepts and topics into a single book.