You would still have the same age, gender, personality, skin color, etc. and you would be able to speak at least one local language and would know basic information of the era and place. Your family, social standing, and such would be randomly picked.
Gay? Ancient Greece. Person of color? Just pick someplace that won’t have significant contact with different races during your lifetime.
what if you’re both?
Then ask someone who knows more about history than me! :)