"Doppio 0" (Double 0) is the italian name of the most refined, totally bran-free wheat flour. Although it usually refers to soft wheat flour, also a "Double 0" durum semolina exists, which is the only one that can be used for the industrial production of dry Pasta according to the Italian law.
"Doppio 0" soft wheat flour is the flour we generally use at home for making both fresh Pasta and cake doughs, and I agree with you that it yields the best results.
Since I make pasta dough only at home and not for professional purpose, I always make it by hand. I also roll it up by hand with my grandma's old king-size rolling pin...but I must admit that this is due to the fact that I'm totally clumsy with the pasta machine and have never learnt how to use it properly :D