EDIT: apparently, the answer below is a 'common misconception'. See the other answers to this question. Learn something new every day!
Yes, there is a spaghetti numbering system. The smaller the number, the smaller the radius of the spaghetti.
For puttanesca, I've seen a suggestion of using #12.
Whether italians worry about this kinda thing - I dunno, but I imagine it depends on the Italian. I haven't run across recipes specifying size yet, and I don't look at it in the store (not even when i was in Italy).
I also have a great illustration for you about number spaghetti. :)