You should learn Finnish. No one does, so anyone you meet will be utterly perplexed and pleasantly surprised. Finland is also closest to Japan from the EU (return tickets $800) and popular in Japan (because of a good school system, the sauna, northern lights, Santa Claus, trendy design, Moomins, etc.)
I'm Finnish and my mother tongue is both Finnish and Swedish. We bilinguals are a 5.5% minority here and Swedish is also an official language. But don't count on being able to use it with regular people, except in the heavily bilingual towns.
Finnish is no way near Swedish/English/German. It's not close to Russian either. Estonian is close to Finnish, but not as close as the Romance or Scandinavian languages are to each other. But Finnish is closer to Estonian than Swedish is to German. Hungarian is from the same language family as Finnish (the Finno-Ugric one IIRC), but they are really different now and neither will help you in the other. I once ate dinner with an Estonian and a Hungarian and we all agreed that Hungarian is totally different.
Finnish pronunciation is really easy and similar to Japanese. We do have the rolled r and umlauts (å, ä, ö), but that's easy because those sounds exist in English (but not in Japanese). For example "ö" can be found in bird/sir/turn/ and "ä" in cat/flat/that. The letter "å" is probably borrowed from Swedish and not used in any Finnish words, only in peoples' names. My Japanese teacher (who is Finnish) told me that Finns in Japan and Japanese in Finland have the best pronunciation in their respective language classes.
There won't be any lack of Finnish material to devour, I think. I don't know about textbooks, but plenty of audiobooks/tv/movies/dubbed anime. Some audiobooks can be found as torrents (on piratebay search for "äänikirja"), for example "Sinuhe Egyptiläinen" (English: "The Egyptian"). That's one of the most famous Finnish books and really good, you should read it in any language. Hollywood made a movie of it in 1954 and apparently it's mediocre. Please read the book instead 
The narrator of the audiobook is Lars Svedberg, who has a really nice deep voice. He also reads slowly, which is perfect for learners. I usually listened to it on 2x speed on my iPod.
The company MOT has good dictionaries, both FIN-ENG and ENG-FIN, which include example sentences. I use their iPhone app quite often.
Do you know the Moomins? They are children's books by a Finnish author made even more famous by the Japanese anime. They are really well dubbed, both in Finnish AND Japanese. The pronunciation is clear, the vocabulary is easy, the speed is not fast and the stories are mature. Check out the Finnish version, then check out the Japanese one. The Finnish episodes are all up on YouTube, but you have to torrent the Japanese ones. Watch these also for your Japanese studies (you'll be surprised at how much you understand)!
Madventures is a Finnish travel show and frankly the best one ever. Yes, I've searched and have found none that even come close. Check out this episode in Tokyo, it has English subtitles as well. You'll have a chance to hear normal spoken Finnish, though with a somewhat Helsinki dialect (the words they use; pronunciation is quite similar across the country). The first two seasons are in Finnish and the third one in English. Unfortunately season 1 has no English subtitles, but the DVD box of season 2 does have English subtitles. You can buy it or torrent it. Even if you have zero interest in Finnish, you will enjoy the show itself!