I'm replacing my folks old thermostat.I'm trying to make sure I have all the information before proceeding. There are 3 wires but only 2 are connected. The 3rd wire is just bent around the opening. So I'm wondering how to proceed with wiring the replacement and what kind of replacement to get. also the furnace is a gas one with a fan[
Generally a thermostat in the most basic sense just completes a circuit and calls for heat. You typically only need two wires for this.
Your furnace probably only requires two wires to call for heat.
Thermostats can also be powered in which case you'd need at least 3 wires or extra wires for extra functions. It really comes down to what your furnace supports and what you want to access from your thermostat. Sometimes you can activate AC with a thermostat as well which could be a separate wire.
I use a tekmar 532 for my radiant hydronic heat it takes 6 wires. 1 for the tekmar network. 2 to complete the circuit (call for heat / activate the zone actuators). 2 for a floor sensor and a neutral as the tekmar thermo is powered without a battery.
I installed an additional 4 wires at each of my thermostat locations for any additional future uses. The tekmar can actually take an outdoor temperature sensor as well (using another 2 wires). I've thought about using two of the wires on a water sensor on the floor which I could hook to a whole house water shutoff solonoid such that a floor in any room causes the water to shutoff to the house.
Your old thermostat likely has mercury so don't throw it into the landfill. I was able to call around and find a mercury recovery place that accepted them for recycle.