1. Assuming, since Helvetica is sans-serif, that you also want sans-serif, the typical fonts are the "Gothic" fonts.
East Asian sans-serif typeface - Wikipedia, the free encyclopedia
2. I'd say the equivalent of a Times (New Roman), a serif, is Mincho, which is very often used in newspapers in Japan, China, and Korea.
Ming (typeface) - Wikipedia, the free encyclopedia Ming is another very, very popular serif font.
3. Neither 音 nor 字 are obscure. They are probably both in the top 100 kanji used in Japanese. Definitely top 500.
4. Finally, there are plenty of good Japanese fonts that come on XP, Vista, OS X, and Linux already. Unless you're designing for Japanese print, you very likely do not need to worry about getting kerning and such right for Asian characters in a western publication. Gothic and Mincho both appear in Windows as MS Mincho and MS Gothic. OS X has Mincho and Gothic fonts as well. Just open Font Book.app and search for "Hiragino."