When I run the thermostat wire for my 2-stage furnace and AC (which I just learned needs an 8-wire line), do I have to worry about wire gauge and wire length? For example, my furnace installation instructions indicate a 24 gauge wire needs 25 feet, an 18 gauge wire would need 110 feet. The furnace is--a straight line distance--maybe 10-12 feet from where I want to put the thermostat. 25 feet of 24 gauge will work for this application?

Yes it will work BUT I would never run that thin of a wire for my control circuits. All we use here is 18 minimum. The cost difference is little or nothing compared to the potential problems with a thinner wire.