Getting a tire without treads is a good way to greatly decrease the effort required to get going and otherwise improve your commute. A narrower tire will also be faster as it has less rolling resistance.

Your primary limitation on tire size is how wide your rim is. I think the only way to check is to measure the width of the inside. Two common widths for a 26" tire are 20mm and 22mm. Here is a chart that shows the tires that would work on those size rims:



As you can see, if you have a 2.1 sized tire you should be able to go as low as a 1.5 regardless of which size rim you have. You should be able to find plenty of puncture-resistant 26x1.5 size tires for rather cheap.

If you want to measure the rim you may find that you can go as low as 1.25" or so. Even with just switching to 1.5" you will notice a big difference.