Installing a high-efficiency furnace (95 % AFUE rating for gas-fired furnaces, 90% AFUE rating for condensing furnaces or boilers) will start to save you money right away.
Also consider electricity-based options, like electric furnaces or alternatives like airs-sourced or ground-source heat pump systems.
Combining the new heating system with a programmable thermostat will maximize the savings that can be made without compromising the thermal comfort of users.