I am working on a japanese website and have a hard time finding a font which looks good in japanese. I was surprised that so few fonts seem to exist for japanese. My team has contacted several web font providers without much success. Only one company could offer a web font for japanese but it was 35 megabytes which is far to big for the clients to download to their browsers.
For Latin letters there are a few fonts which one can be quite confident almost all users have, like Arial, Verdana, TNR, Georgia and so on. What fonts equal these in japan?
Web-font for Japanese, though there are few providers exist, is not really practical as you found the size of the font data is too big to download. Usually Japanese font has 8,000-16,000 glyph so making new fonts means you need to make at least 8,000 glyph, which is pretty heavy task. As a result of it, there are very few variations in Japanese fonts, and Japanese users also care about fonts less than Latin-character users.
Most Japanese websites use default font sets provided on Windows or Mac. The latest ones are Meiryo and Hiragino Kaku Gothic Pro. For older versions such like Windows XP, it is good to add former default fonts MS Gothic(or MS Mincho)/Osaka.
Some old browsers could not understand those font names in English, some others do not recognize the names in Japanese, so it is safe to write both in Japanese and English.
Meiryo and Hiragino's order is, because Mac users may have Meiryo from MS-Office, and Hiragino is more familiar and matching well on Mac, better by starting Hiragino series.
So the current recommended practice is like this,
font-family:"ヒラギノ角ゴ Pro W3", "Hiragino Kaku Gothic Pro",Osaka, "メイリオ", Meiryo, "ＭＳ Ｐゴシック", "MS PGothic", sans-serif;