Imperial Roman History traditionally begins with Julius Caesar (or his assassination) and ends with the usurpation of Rome by the barbarian Odoacer. These five books -- some to keep as reference, some to read from cover to cover -- will provide you with an excellent foundation for further study of Roman imperial history to the fall of Rome in A.D. 476.
If you're looking for a thorough, basic book on the fall of Rome from a modern perspective, Peter Heather's The Fall of the Roman Empire
would be a good choice. It has its own agenda, but so do the Christianity-focused (Gibbon) and economic-focused (AHM Jones) classic works on the fall of Rome.
The first three volumes of Edward Gibbons' masterful history of the Roman Empire cover the period from A.D. 180 - 490, from the reign of Marcus Aurelius to Odoacer and the "fall" of the western Roman empire. Although two hundred years old, much of his research is still valid.
The 12 Caesars are the emperors of Rome from Julius Caesar to Domitian. Translator Robert Graves of "I, Claudius" fame, animates the gossipy biographies of Suetonius who tries to provide balance with a good side of even the most lusty, villainous emperors. A fascinating look at which behaviors were acceptable and which led to assassination.
More than just a heavily illustrated look at the emperors of Rome, this is a useful reference for comparing periods and individual imperial deeds and accomplishments. Pleasantly written and browsable.
Roy A. and Lesley Adkins' "Handbook to Life in Ancient Rome" is not limited to the Imperial period. This handbook covers mundane details of Roman life, as well as the Republic, military affairs, geography, town and countryside, travel and trade, writing, religion, economy and industry.
Last only because such a short portion of Imperial Rome is covered (the Julio-Claudian emperors), Howard H. Scullard's history explains the social turmoil of the Republic that fermented and became the Empire.