Can I run power from a GFCI receptacle to a standard receptacle then to a light switch?
In general, yes.  GFCI outlets have LINE and LOAD terminals.

You can connect several more outlets on the LOAD terminals, and they will also be protected from ground faults.

You can also add a switch, though bear in mind that highly inductive loads (like a large motor) can cause nuisance tripping of the GFCI.