CJK languages use a lot of different characters at a time and that makes font development more difficult, but that doesn't mean there is a shortage of choice.
Here is a page full of free-for-commercial-use Chinese fonts (simplified form), for example.
Your first priority is to settle on an aesthetic. Show your current font to your translator and have him/her give you suggestions. Or alternatively, since CJK fonts typically come standard with a matching basic ASCII set, you can select the font based on how it renders English, and the result in Chinese/Japanese would look similar to a native speaker.
With Chinese in particular, pay attention to whether the font is for simplified form or traditional form, and match it to your translation and audience needs. Some fonts have both, but others have only one or the other, and that could be source for trouble with blanks. For example, if you plan to use Google APIs, a traditional form translation would be warranted because Google is inaccessible for a majority of simplified form users. Your translator should advise you on these factors.
Finally, you need to know that CJK is hostile to surface-based fonts, and demands that you use
font_add(). See
this old example for how to handle it properly.
