I need to buy some screws and springs for connecting pieces to a core. I know you guys recommend M3 or 4-40 machine screws, but you can also buy complete sets from cube4u or hknowstore. Has anybody used these sets before? Which are the best ones? What size hole do I need in the core (for M3, I think this is 2.75mm, but what is it for the sets)?

I use the springs and small washers from this package: http://9spuzzles.com/index.php?gOo=good ... oductname=
Unfortunately, the big washers and screws are no good. They force you to design center holes much larger than regular M3 screws which results in a much larger puzzle overall. If you do want to use those screws then a 2.75mm hole will be fine as well.
I use M3 screws from Fabory and combine them with those small washers and springs from 9s.