I do not know what color wires I need to connect to the new thermostat. And I am not sure if the one I bought will work?

Model number and braned purchased ?
Model number and brand of furnace?

There is a great explanation of thermostat wiring at https://www.askmehelpdesk.com/heatin...ons-58313.html

It also has ''do I have a heat pump?''. They require more complicated thermostats and wiring.