Just my view, but ...
I typically write down the ratings before the game ... most of the time you know these and won't necessarily know the ones after the game.
I typically regard the signature spaces as "white on the left" and "black on the right" so I would first sign the sheet based on the color I had, then hand it to my opponent to sign in the other space.
There may be other views of this, of course.
I just had my new score sheet (http://www.jrobichess.com/downloads/chess_score_sheet.JPG) from "jrobichess" and I would like to ask what should I write in the ratings? Should I write the ratings of the players before or after the game? Because here in chessdotcom when you look at your recent games in live chess, the ratings displayed are based after the game itself so I don't know what to write in the ratings tab... One more thing, just to be more specific, how should I know where to write the signature of the players? Based on the above link, where should the white player sign? so as the black? Should it be on the left or right signature tab? <sorry for my bad english>