Reading:
Greek Historians from M. I. Finley's Portable Greek Historians (Penguin):
Herodotus (Latin); transliterated: Hêrodotos; Beta Code *(hro/dotos=Hera's (or Hero's?) Gift (ca. 485-430 BCE), Histories (i(stori/ai, "investigations"). Selections from book I (on Lydia), II (Egypt) and VII-VIII (war of Xerxes' Persians against the Greeks, after Marathon). See me for exact selections if you're using other translations. Greek and English available through Perseus and English through the Internet Classics Archive, or the Internet History Sourcebook at Fordham.
Thucydides=Thoukudides=*qoukudi/dhs=Child of God's/Goddess's Glory (ca. 456-400), Peloponnesian War. Selections from book I, II (Funeral Oration and Plague), III (Mytilene and Corcyra) and VI-VII (Sicily). See me for exact selections if you're using another translation. Greek and English through Perseus; English at ICA or IHS.
Polybius=Polybios=*polu/bios=Much life (ca. 208-126 BCE), History. Selections from Book I (scope of work) and VI (Roman constitution). Further selections in Mellor (see Roman Historians below). E-text at Perseus.
Biblical Historiography from any edition of the Hebrew Bible (Old Testament) and New Testament. Bible. E-texts and lots more in Torrey Seland's [Volda University, Norway] Resource Pages): Genesis (J document ca. 950BCE? D additions ca. 600, P 400 or after), I and II Books of Samuel (Early Source ca. 950), Ezra and Nehemiah (ca. 400), Daniel (ca. 164), Gospel of Mark (ca. 60 CE), Acts of the Apostles (before 100 CE)
Roman Historians from Ronald Mellor's The Historians of Ancient Rome (Routledge):
Biography. Plutarch, Ploutarchos *plou/tarxos "Wealth rules" of Chaeronea (and a priest at Delphi) c. 45-125 CE, Lives. Selections from the Modern Library ed., volume II. We can consider also whether a Gospel is in some way a Life, and also look at C. Suetonius Tranquillus' Life of C. Caligula, Tacitus' Life of Agricola and Augustus' Res Gestae (Achievements) of the Deified Augustus, all from Mellor's anthology.
Sather Lectures on historiography by the uniquely qualified Arnaldo Momigliano (1908-87), The Classical Foundations of Modern Historiography, Univ. of Cal. Press 1990 (lectures delivered 1961-62: 1992 appreciation by Donald Kagan). Lectures on "Persian, Greek and Jewish Historiography", "Herodotean and Thucydidean Tradition", "Antiquarian Research", "Fabius Pictor and National History", "Tacitus and the Tacitist Tradition" and "The Rise of Ecclesiastical History".
Other materials as you find them in the Library or on the Internet.