Which is better for the enviornment? Using a gas furnace or a lot of electric space heaters?

Depends how you use them. Electric space heaters are less efficient but can be turned off - you can leave certain rooms cold and others hot at certain times of the day (ie, when you're sleeping or at work). A furnace will heat either all of the house or none of it, so its more difficult to micro manage.

This is difficult to answer because it depends on the source of the electricity and how you define "better for the environment." If they burn coal to get power then there is more CO2 burned with the direct burning of coal than natural gas. However, natural gas has a lot of water contamination issues associated with it (http://www.gaslandthemovie.com/) If your house is powered by solar and / or wind then it's certainly better for the environment to use the electric.

In general, you're going to pay more for using the electric than the gas. With that additional saved money, you could always invest that in something that's good for the environment - like stuff for your garden or buying local organic produce, investing in wind / solar, or any other number of things.

gas furnace. electricity for heat is usually much more expensive than natural gas.