Yes, he tells the story about the time and context so well that you don't need any background knowledge. All his books are about people and power, which I think anyone can learn from.
...if so, which one would you start with?
I would recommend starting with Master of the Senate, since I think it's his best work. But I started with the first in the LBJ series and it's incredibly gripping as well.
The Power Broker is also excellent and absolutely worth reading, but in my view not quite as good as the LBJ series.
The Power Broker has one great strength over the LBJ series: concision.