The set screw for the handle went down the drain what size set screw do we need.

Who knows. Take the handle to the hardware store, Home Depot or Lowe's. In the isle of the nuts, bolts and screws you should find a cabinet with set screws. Select one that fits.

If you have another same faucet in the house remove the screw from that one and take it with you to a hardware store if not do as Hkstroud suggested, good luck.

John