Should I install a gas furnace or a heat pump?                         

Let's break this down by climate:

Extreme northern climates.. Natural or propane gas wherever possible.

Cold Climates...Natural gas if available or a heat pump with bias toward gas.

Moderate climates... Natural gas or a heat pump without bias one way or the other

Extreme southern climates... Heat pump, electric heatstrip or natural gas if available. Of course, a heat pump system includes air conditioning as well.