CJFusco,
I work in the bike industry and commute almost daily by bicycle. Most of the advice you have gotten here is legit, but I will add my $.02.
First, stay away from department store bikes. The main problem, besides not ever being put together correctly, is the bearings. We're talking hubs, headset, and bottom bracket here. Crap components will be noisy, ride poorly, and go out of adjustment often. IMO a bike with crappy rotating components will be miserable to ride for anything more that a mile or two. If you are looking at a fifteen mile round trip, you will appreciate the nicer quality stuff. Think of it this way: on a bike, there is no ipod or radio to distract you while in transit. That means that you hear and feel
everything, and a clicking bottom bracket or wobbly headset will drive you absolutely crazy in no time.
Next, I agree on the mountain bike with skinny/high pressure tires idea. The bike will be much more robust, and you won't fret when a pothole appears out of nowhere. If you are running flat/riser bars, consider a set of bar ends. While no longer in vogue, they really do allow you to stretch out and have a couple of different riding positions.
As far as the single speed/fixed gear vs. geared bike argument, I prefer gears, even though single speeds and fixies largely pay my salary. I do commute on my single speed every once in a while, but for longer trips I take my geared townie.
Also, instead of a rear rack (panniers can be nice, but I prefer them on the front), I recommend a front basket. The weigh distribution is usually better, and you don't have to worry about bugie cording everything down. Not that I am biased or anything, but this is a nice one:
Finally, CL is your friend. You should be able to find something cheap with nice components. At 5'8, I'd look for a 17" frame.
Good luck,
Jim