For ancient Egyptian history, I strongly recommend beginning with a recent book like Temples, Tombs, and Hieroglyphs and Red Land, Black Land by Barbara Mertz, The Rise and Fall of Ancient Egypt by Toby Wilkinson, or The Story of Egypt by Joann Fletcher.

Durant was an armchair historian with no Assyriological or Egyptological training, and his book on the ancient Near East wasn't very good or up to date even when it was written about 90 years ago, and it's now wholly obsolete. It was written before the decipherment of ancient writing systems like Linear B and Anatolian hieroglyphs as well as before key archaeological discoveries like the Early Bronze Age city of Ebla and the Neolithic town of Çatalhöyük. Even the information Durant includes is often wrong or outdated, such as referring to the site of Ugarit as Zapouna.

Breasted's works are a very different kettle of fish. Breasted was an excellent philologist for his time, and his translations of monumental inscriptions (Ancient Records of Egypt I-IV) are still fairly useful despite advances in our understanding of the Egyptian language. There have been many textual and archaeological discoveries since Breasted's time that have radically changed our views of Egyptian history, however, such as Barry Kemp's excavations at Amarna, the Austrian excavations at Avaris, and the ongoing publication of texts like the Deir el-Medina ostraca and Tebtunis papyri. Additionally, Breasted (like all historians) incorporated personal biases into his work. For example, his discussion of the priesthood of Amun in Development of Religion and Thought in Ancient Egypt - and his clear distaste for the institution - is colored heavily by Breasted's Protestant background and opinions on the Catholic church.

Thutmose III seems to have merged the priesthoods of all the temples of the land into one great sacerdotal organization, at the head of which he placed the High Priest of Amon. This is the earliest national priesthood as yet known in the East and the first pontifex maximus. This Amonite papacy constituted a powerful political obstacle in the way of realizing the supremacy of the ancient Sun-god...

Breasted also had some highly questionable views on race and ethnicity. His son Charles Breasted quotes him in Pioneer to the Past:

Undoubtedly a certain amount of new blood is stimulating and beneficial. But what shall determine the proper amount? American industry's need for cheap labor? A blouse of Congress thinking of the nation's future in terms of the next election? Our theoretical sociologists? Inevitably we shall close our gates too late. It remains to be seen whether the creative contributions of the Schurzes, Steinmetzes, Michelsons, Pupins and their rare kind, and the solidity of the better farming and lower middle class elements from northern Europe can offset the retarding effects of the great unassimilable masses of Mediterranean and eastern European populations...

Along the same lines, Breasted remarked in The Conquest of Civilization:

The population of the Great Northwest Quadrant, from the Stone Age onward, has been a race of white men of varying physical type. The evolution of civilization has been the achievement of this Great White Race...

On the south of the Northwest Quadrant lay the teeming black world of Africa, separated from the Great White Race by an impassable desert barrier, the Sahara, which forms so large a part of the Southern flatlands. Thus isolated and at the same time unfitted by ages of tropical life for any effective intrusion among the White Race, the negro and negroid peoples remained without any influence on the development of early civilization. We may then exclude both of these external races - the straight-haired, round-headed, yellow-skinned Mongoloids on the east, and the woolly-haired, long-headed, dark-skinned Negroid on the south - from any share in the origins or subsequent development of civilization.

We now know that this is complete nonsense, and in fact ancient Africa had numerous civilizations aside from Egypt. The history, art, and archaeology of Nubia is no less fascinating than that of Egypt, for example, as has been outlined by recent publications like The Black Kingdom of the Nile by Charles Bonnet, Ancient Nubia: African Kingdoms on the Nile edited by Marjorie Fisher, et al., and the MFA catalogue Jewels of Ancient Nubia.