Ideal screw type depends on the blind and how its being fixed.
If fixing a roller blind back to a UPVC or Wooden window frame then use a 12mm x no8 self tapping screw, ensure you pilot first to ensure that the screw does not run of to one side when tightened.
For fixing with a rawl plug use a good quality No 4 x 40mm wood screw, you can use 30mm with some rawl plugs but check their specification first.
If its a damp area then you may wish to consider a stainless steel screw to prevent corrosion but be gentle as they are more brittle than a normal screw.