Marcie,
Your approach is sound, many "hang" a shelf from the Rafters.
As far as the quantity of screws, as Jeffie says, it depends on the condition of those Rafters. You'll need a "Stud Finder" to get a good Center for the Screws.
The more screws the stronger, and I've "Pre-Drilled" the screw holes on many occasions, just to make sure i was in solid wood, and that the screw went directly into the center of the Rafter.
You're looking at 1.5" of 2x4 & 1/2" of Sheetrock, so double that for the serew length.
A #10 or #12 diameter screw should work fine.
I've used Phillips Head just for convienience, electric drill um in.
Have a good Day !
S.W.