General Classical History
For accessibility and range of topics, two modern writers of ancient history stand out: J.B. Bury and Michael Grant. Bury's nineteenth and early twentieth century authoritative works are available in Modern Library Giant and Dover publications. Michael Grant's works are available in a variety of editions, and his name is featured in the foreword or as an editor/translator of many other books.
Democracy and Political Theory
An approach to ancient history is to explore one of the many subtopics. Since Athens is associated with the birth of democracy, political philosophy is a good one. You can start with Plato; then on to Machiavelli and to the present. Many writers have an agenda and write to support it. This is less true of academics -- like the interesting, persuasive Donald Kagan, who, nonetheless, bothers some because of his modern political affiliations.
Women in Antiquity
Popularity has some merit. If nothing else, you'll read along with everyone else. Lefkowitz, Fant, Keuls, and Pomeroy are among the writers about ancient women works are still available in reprint. For information on specific women other than the famous queens of Egypt, for which, see Tyldesley, your choices are limited. Generally, look at the author's credentials and what else she has written. Read reviews.
In addition to the polytheistic religions familiar from the Mediterranean area, the monotheistic religions of today got their start in ancient times. For those interested in the origins of Mithraism, Biblical Archaeology recommends David Ulansey. Timothy Gantz' Early Greek Myth is a winning reference. For more readable material, try the Adkinses' books or Michael Grant or C. Kerenyi. For those with a higher budget, look at the Wiley-Blackwell books.