Should I replace my mercury switch thermostat?
Almost every thermostat on the market today is a better alternative than a mercury switch-type. 

Even the cheapest digital thermostats have schedules, so that they can have different heating points during the morning, daytime, evening and overnight, and range from having weekend vs weekday to 7-day indepedent schedules. This allows you to save money by turning down the temperature while you're not home or sleeping. 



On the more advanced side of things, there are internet-connected thermostats you can program/control from your PC/phone/etc, and ones that can self-learn based on manual adjustments and motion-sensing. There is a corresponding increase in price, and these typically do require a C-wire so since you only have two wires you'd have to pull a new wire for this.





To connect a basic digital thermostat to the 2-wires, the best thing is to follow the instructions that come with the thermostat. Typically you're going to connect the two wires between R (or Rh) and W.