In the years around 1960, George Sansom published the three volumes of A History of Japan. Are they still OK for reading about the basics? If it matters, I'm not likely to go any further into Japanese history -- I just wanted to read something with some meat but that's an overview of a variety of topics.
Sansom's reputable as a source for an overview, though of course you'd get more information if you looked into specific texts (though this probably isn't what you want). Similar to what /u/ParkSungJun said, since the 1960s there would be development on certain schools of thought regarding history. Also, from what I've heard, his series are rather dry and barebones.
For what you describe, I'd recommend Japan Emerging by Karl Friday instead, which splits the entire history of Japan into smaller timelines which are built upon or otherwise refined by specialists, and then compiled into one. A best of both worlds situation, and it's much more recent, unlike Sansom's A History of Japan.
Sansom has a bit of a reputation for being a Japanophile, so there is definitely a bit of bias on his part, and also there have been some more recent theses about various elements of Japanese history that may have changed since the 1960s (I am thinking primarily of some more revisionist views of the Sengoku warlords) but overall he is a good source for some of the basics.