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.
As a gay man, maybe early empire Rome? Or even like early nomadic tribe times? Like, before there were institutions large enough to oppress people en masse. I’m sure there was plenty of gay sex happening as a nomadic hunter or trader.