Traditional Chinese or simplified Chinese?

Pick a good Latin + Cyrillic family and find a separate Chinese typeface that complements your choice. Otherwise your options will be severely limited.

But quite a number of Chinese typefaces do throw in Latin and Cyrillic and Greek as afterthoughts. That the choices of style for those other languages will be severely limited, though, is true - while "almost any Chinese font" for the appropriate coding scheme will support those languages, they won't necessarily do it well.