Let's get a list going of primary texts which NT scholarship should be more familiar with! I'll start with: (1) Fragments from Hellenistic Jewish Authors (4 vols.). Some awesome stuff in here!

(2) The Elephantine Papyri. A group of Jews living in Egypt worshipped a god they called יהו and looked very different from the Judaism many NT scholars are familiar with. 10/10 would recommend. https://brill.com/view/title/508 

(3) Piyyutim—Hebrew liturgical poetry, many written during rabbinic era. Texts are scattered throughout various mss, some collected in Hebrew volumes (e.g. https://www.bialik-publishing.co.il/index.php?dir=site&page=catalog&op=item&cs=341). Limited English anthology here: https://www.psupress.org/books/titles/978-0-271-02357-1.html

(4) Corpus Inscriptionum Iudaeae/Palaestinae (h/t
@collincornell1). The title says it all. https://degruyter.com/view/mvw/CIIP-B 

(5) Greek Magical Papyri (h/t/ @JeremiahCoogan). Spice up your research with some curses, spells, and love charms. Online: https://digi.ub.uni-heidelberg.de/diglit/heidhs3763IIA-51bd1 . Print: https://press.uchicago.edu/ucp/books/book/chicago/G/bo3684249.html

(6) Tal Ilan, Lexicon of Jewish Names in Late Antiquity (4 vols.) (h/t @collincornell1). Ancient Jewish names can tell us a lot about ancient Judaism! Vol. 1: https://www.mohrsiebeck.com/en/book/lexicon-of-jewish-names-in-late-antiquity-9783161587931?no_cache=1

(7) Aramaic Incantation Bowls. Watch out for the evil eye! https://brill.com/view/title/38923

(8) Menahem Stern, Greek and Latin authors on Jews and Judaism (3 vols.). (h/t @ymiller419). If you want some outsider opinions on ancient Jews, this is your one-stop shop!

(9) Early Greek Mythology: Iliad, Odyssey, Theogony Works & Days, the Homeric Hymns. "These writings dominated the discursive reservoir of that tiny male selection of Greco-Roman population that could produce the levels of texts seen in NT"— @SLYProfessor. Get to know these well!

(10) Textbook of Aramaic Documents from Egypt. (h/t @ymiller419). Cut your teeth on some Imperial Aramaic and get a look into the nitty gritty of people's lives (marriage docs, oaths, court records etc.) https://www.magnespress.co.il/en/book/Textbook_of_Aramaic_Documents_from_Ancient_Egypt_Vol_1_-_Letters-3651

please everyone add your own contributions!