Reddit reviews The Kojiki: An Account of Ancient Matters (Translations from the Asian Classics)

I'll do classical works, since those are what I know best.

Classical works:

Kojiki. One of the recent translations is highly readable. It contains the major native myths and legends, which you will see referenced over and over again in your modern works.

Manyoshu: Earliest surviving collection of native poetry. A partial translation done in the 50s is the one I recommend, as the final English was worked over by an actual English language poet, making it by far the most accessible one around. Poets and topics range far and wide, especially when compared with later classical works.

Tales of Ise: Another one with a recent translation. Provides a good look at the noble aesthetic, romance in classical Japan, etc.

Kokin Wakashu: There are no easy to find translations of this, unfortunately. However, if you were to ask a Japanese scholar what the definitive Japanese classic is, this would be it. All later aesthetics, from literature to art, derive in large part from it in one way or another. It is a collection of poetry from 905 (approx) that epitomizes the new noble aesthetic of the age, and as I said, sets the tone for the next millennium and beyond.

Tale of Genji: The definitive prose classic. Courtly love and romance, political intrigues, all that. There are several full-length English translations (and a few that aren't full length). There are still many adherents to the Arthur Waley version, despite its age. The newer Royall Tyler translation is more thorough and scholarly accurate, however.

Tale of the Heike: Several translations exist, but the recent one by Royall Tyler does a good job of projecting the lyrical quality of the original while maintaining accuracy. Several others exist as well, but the Tyler is probably the easiest to both find and read. Tale of war and upheaval at the end of the 12th century, showing the decline of the nobility and rise of the new warrior class. Probably hard to go from cover to cover with, as there are many names/events/places that are hard to follow for most readers. Spot reading recommended.

Confessions of Lady Nijo: There are a few translations, but the one I have linked is probably the easiest to find. Discusses the life of a woman who served in the imperial courts of the late 13th/early 14th C. and all the trials and tribulations she faced by receiving the favors of the emperor.

Hope this is a good start for you all.