I highly recommend Fog of War.
Although it's mostly biographical from Robert McNamara's perspective, it's a fascinating (and I don't use the term lightly) look at the type of people and decisions that lead the country to war. It puts a human face on those decisions and made me realize that as smart as the policy-makers may be, they're still just flawed humans who can make terrible mistakes. McNamara seems not to worry much about making mistakes that lead to thousands of deaths, and he tries to distance himself from some of his decisions. But he does admit, now that he's 85, that he might not have been right about everything.
I don't know much about LBJ, but from the conversations between him and McNamara, I don't have much respect for the man. To think -- America got stuck in Vietnam because LBJ and others wanted to "kick some ass" and send a message to the Ruskies? Hmm...
There are obvious parallels to the current administration that are reason enough to check out the movie. If you get anything from the film, it should be a healthy dose of skepticism. Too often we're asked to take for granted that our president, the secretary of defense, and other policy wonks actually know what they're talking about and are making good decisions.
Fog of War shows how even a very bright man can influence history and cause catastrophic consequences. He says himself that we came "this close" to total nuclear war. Only luck saved the world.
That doesn't inspire a lot of confidence.
As a side note, Philip Glass's score is not bad (though typically formulaic). There's something about his music that makes a 2 hour film feel like 10 hours. And that's coming from someone who likes his stuff.