I agree that gears are helpful for a new commuter, even on a relatively flat 20 mile rt commute. There's also wind, and if you're riding for ten miles into a steady wind, you might as well be going up hill. Also, you might want to take your bike to other, hillier terrain. I understand the appeal of ss, but I'd go for a geared bike.

Fenders are great for the muck, and some of what you'll need will depend on whether you can change at work. My winter commuter is a mountain bike. The rack on the back serves pretty well as a rear fender (not perfect, but it keeps me from getting the old skunk stripe), and because I do have front suspension (liked the bike when I bought it used and haven't switched out the fork, but I agree with Slim that rigid is better for your purposes) a full fender was hard to find for my front wheel, so I got a mudguard that screwed into my headset from the bottom. Works great.

Here's the main thing--have fun, be safe, get a bike you like, leave yourself time and don't be afraid to ask questions or give yourself a break when you need one. If you're like me, you'll look forward to your commutes days in advance and feel happier, more alert, more energetic and prouder all day long. All the rest is just details.