* 文化 (bunka): This is the most common and general translation of "culture." It refers to a society's intellectual, artistic, and social achievements and traditions.
* 文明 (bunmei): This means "civilization" and is sometimes used interchangeably with "culture," but it emphasizes material progress and societal development more.
Therefore, the best kanji spelling depends on the context. For most general uses, 文化 (bunka) is the correct choice.