Fixed gear and single speed drive trains can be a lot of fun, especially in the city, and I use both on my flat 30 mi RT commute. However I don't think it's worth spending much money on them, and I wouldn't want one as my only bike. If you do want to start going on longer rides, or riding with a club, it'll hold you back. I've done a century on a single speed (out of necessity, my geared bike was in the shop), and I have no desire to do it again.
Still, I love ss/fg bikes for the city. If I were you, I'd buy a new road bike and cobble together an ss/fg from an older road bike. If you're the slightest bit mechanically inclined, making your own ss/fg from an older road bike is really satisfying and very easy.