I did not really consider learning a novel before, but Murakami is not a bad idea, thanks ! And I like his novels, too. It is just that I would rather learn a real classic of Japanese culture, which makes it more worth the pain. Maybe Kawabata would be more satisfying in that regard. Or Mishima ?
Also, a novel will be much harder to learn than a poem, which has rimes (or similar play with sounds) and rythmes in it. My first choice (by far) would still be a long, classic poem, and my second choice a classic novel. So I am still open for suggestions!
Also : I am well aware of the difficulties to read the text in Japanese. It would be important to have a digital version, so I can easily use the various tools on Internet to read it. [That is a fifth requirement I forgot : a digital version of the text should be available!]. Yes, textbooks is a possible tool among others, and also asking some natives to check that I'm not mistaken.
As for the method, it is inspired by the wonderful story told in The Ignorant Schoolmaster, by Jacques Rancière. Beyond what it suggests about learning foreign languages, it is a wonderful philosophical reading so I warmly recommend it.
Many thanks