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.
Lincoln’s booth in Ford’s theater on the night of the assassination right before it happens. Saving the president will immediately give me some credibility and influence, and it could improve reconstruction of the south to an extent that positively impacts modern America.
It may complicate your life though. You’d have no explanation of who you are or why you’re there.