公主 (gōng zhǔ) - This is the most common and literal translation of "princess." It literally means "noble lady" or "female ruler." It's used for princesses in general, both real and fictional.
王妃 (wáng fēi) - This translates to "queen consort" and is used specifically for the wife of a king. It's less common than "公主" to refer to a princess.
郡主 (jùn zhǔ) - This translates to "princess of a county" and is a more specific term for a princess of a particular county or region.
小公主 (xiǎo gōng zhǔ) - This translates to "little princess" and is used for young princesses or for a more informal and affectionate way of referring to a princess.
So, the best way to spell "princess" in Mandarin depends on the specific context and the specific nuance you want to convey.