For me it really depends how good a story of the game is for me. Some games drag the story way to much but have some good scenes, so i sometimes just skip some dialogue if i don't find it interesting.
I don't know if it was really my first but the most memorable one of the firsts was for sure Being a DIK and it might have been a mistake beacause now i am chasing that feeling i had when i played that game for the first time and i don't think any other game will be the same.