It's been awhile since I've been out of academia and even longer since I've studied the Han Dynasty, though much of my coursework in graduate school had to do with early and medieval China, so I'll give my thoughts on this. Mark C. and others my have different views. First of all, the Shiji is the first of the three books you mentioned. It was written during the reign of Emperor Wu of the Han by Sima Qian, continuing the work of his father, Sima Tan. There is a reason why it is different then most of the later official histories, which are histories of dynasties or parts of dynasties, usually written during the subsequent dynasties. Sima Qian's mission, as he saw it, was to write a history of everything up to his own time. But he wasn't simply recording facts in the sense of modern history; at least one of his tasks was to uncover the heroes of the past who had been forgotten, and once you know a little about his autobiography, it is difficult not to read his own situation into many of the historical events he relates. See, his boss, Emperor Wu, gave him the choice between death and castration. He chose castration, apparently so he could finish the Shiji. You can find an excellent account of this in Stephen Durant's The Cloudy Mirror: Tension and Conflict in the Writing of Sima Qian.
The Shiji is the model for all later official histories, but in my mind it has more literary value than most, and it's a lot more than history.

As Mark C. points out in the thread below, what you are calling Tseen Han Shu (Qian or Ch'ien are preferable to Tseen) is usually referred to as the Hanshu, or the History of the Former Han. As the title suggests, its focus is the Former or Western Han, when the capital was in Chang'an (modern-day Xi'an, though much larger, at least during the Tang, when it was also capital). The Houhanshu, written well after the fall of the Han, tells of the Later or Eastern Han, after the capital moved eastward to Luoyang. You can find a little more about other histories of the Han here.

I'm not as good with the Tang, since the Tang never interested me as much as some of the other periods. I don't know why that is. Sorry, I can't help to much with An Lushan.

I'm not sure I can say which histories are the most reliable, and I would never take the word of just one of the histories. Even the Shiji is not necessarily more reliable, though unlike most of the later histories, Sima Qian wrote at least some of it about his own time, and he allegedly visited many of the sites about which he wrote. As for the later histories, even though they were written during subsequent dynasties, they often use sources from the actual dynasties, though many of these sources either have not been translated into English, or are no longer extant. Hope this is helpful.