What is the best heating system for a 1,600 sq ft house?

Depents on your budget. Gas is less expensive than electric overall on a monthly basis but if you do not already have existing gas lines in your house could be costly in the initial stages.

The square footage is not enough to answer this question - better call a local reputable HVAC company and schedule an appointment with them. So they can look at your current system, check ductwork (if any) perform proper heat load calculations to find out the right size of the equipment, check for air leakages, etc.
However - avoid the companies who will just come to your house, check existing model numbers/sizes and will try to match new equipment based on this information.