Oliva is my all-time favorite player, but I didn’t go to my first Twins game until 1977, so it would have to be him.
Otherwise, Joe Nathan. Aside from the “pfbfbfbfb” thing when he was on the mound, he was a welcoming autograph signer for my young sons, usually posing for pictures as well. I also always got the sense that he set the tone for others, who figured that if the superstar willingly signs, they could too. I’m talking about Juan Rincon, Jose Mujares, etc.