In case you’re interested, the Tofugu team did a couple of interviews with some translators or interpreters. Feel free to check out their podcast:
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Tofugu - What Makes a Good Japanese Translator? feat. Alexander O. Smith
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Tofugu - Translating Historical Texts (That Have Never Been Translated Before) feat. Matt Alt
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Tofugu - Interpreting for Osamu Tezuka feat. Frederik Schodt
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Tofugu - Do You Have What It Takes to Be a Freelance Japanese Translator? feat. Nora Stevens Heath
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Tofugu - Stories from Translating Final Fantasy X feat. Alex O. Smith
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Tofugu - How to Get a Job at a Japanese Video Game Company feat. Ben Judd
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Tofugu - Learning Japanese and Secret Ways to Visit Japan: Advice from Loretta “Kemushichan” <= technically not a translator but might be still interesting as she seems to be very popular
The different book clubs here in the forums have been mentioned already, I think. Definitely would like to second them 
Also, I’d like to propose to have a look into Becks’s intensive reading/study log. They are not a translator but they tackle native material step by step. Maybe you can find some ideas or techniques to get you started.
Another one I’d like to throw in is JSTOR. They are not limited to literature so you can find a lot of different articles, journals and so on in there.
As for Japanese literature: in case you want to get an overview and are not sure where to start Donald L. Keene has published a couple of well known works in this field. It might give you a good background in canonical classical and modern Japanese Literature.
Also, you can have a look into 国際芥川龍之介学会 (International Society for Akutagawa [Ryunosuke] Studies). Their work of field is very specific though 
Something I noticed after taking two semesters in Japanese Literature is that ~ like probably everything ~ it is the entrance of a rabbit hole. After this I took classes In Japanese History… and then politics and then I wanted to learn about some modern Japanese thinkers… So, you might not be limited to Literature. And I think it was Nora Stevens Heath who, during the podcast with the Tofugu team, elaborated a little bit on her specialty ~ not being specialized.
I’m sure, which ever road you take, getting some basics in these topics will help you to understand why certain topics are addressed from certain angles. Or it will help you to catch references and so on.
Good luck with your further studies and as others already mentioned feel free to keep us posted 