How to do with an unused C wire when installing a thermostat

You're going to have to take a look inside the furnace, where you should find the control board where all these wires terminate. Each terminal on the control board should be labeled, so just make a list of letters and colors. Then go back to the thermostat, and use the list to connect the wires to the proper terminals.

If you post the make and model (model number would also help) of the furnace, or a quality picture of the furnace wiring diagram (should be printed on the inside of the access panel), somebody may be able to offer a better answer.

I would remove the jumper from Y to G and use your yellow for Y.

On the thermostat and the furnace you should have Y , yellow (cooling) G, green (fan) R, red (power 24v) jumper R to Rc, Rh W, white (heat) no jumper, on thermostat use W1 (first stage heat). Leave W2 unused and set the thermostat to single stage heat, single stage cool, that way the thermostat knows that there is nothing connected to its W2 terminal. C, blue (common/ground) this wire allows the thermostat to draw power from the HVAC system as opposed to using the batteries.