1 inch = 25.4 mm. If this is your outside measurement, then the true rim width (which is measured on the inside from bead hook to bead hook) is likely 23mm. If I were you I would measure the inside dimension so that you know what you have. If you don't have access to a caliper, take a thin piece of cardboard, and keep trimming it down until the cardboard just touches the bead hooks. Then, measure the length of the piece of cardboard.
If you in fact have a 23mm rim (technically would be a 559-23), then the narrowest tire that you'd want to install is a 37mm tire. Anything narrower, and you're going to run the risk of blowing the tire off the rim when inflated to max pressure. If it's a 21mm rim, then you can get away with a 35mm width tire.
It appears to me that Continental does not make the Ultra Gatorskin in a wide enough version for your rims (someone correct me if I'm wrong about this). The Marathon that you linked will work, I've also read on these forums that the Pasela TGs and Pasela Ribmos are well liked.
Your best bet may be to look through some of the tire threads that already exist on Bike Forums (there are plenty) and see what people are saying about their tires. Make a list, and then check with the manufacturer websites to see if thes tires are made in the size(s) that you need. If you have any specific questions about Schwalbe tires, I'm happy to provide answers. If I know anything about the other brands, I'll let you know that too.
If I were in your situation, one of my major considerations would be puncture protection. Doesn't matter how fast a tire rolls if you're getting a flat every 3rd day. The distance you are now riding increases the odds that you'll have some unpleasant patches of roadway on your commute. When you're looking at tires, be aware of what type of puncture protection they have. A good aramid (kevlar) belt is generally sufficient unless you have some really gnarly debris to deal with.
Here are some links that discusses tire and rim dimensions:
http://www.schwalbetires.com/tech_info/tire_dimensions
or
http://www.sheldonbrown.com/tire-sizing.html