#kilott
The Kilo TT pro from bikes direct is possibly the best bicycle for the money that can be had anywhere. It is $400. You may be able to find one used on craigslist, but I strongly urge you not to do three possible things that you might think were cheaper. 1. Please do not get a cheap bike off of craigslist thinking that you will be able to convert it to fixed gear for little money. Conversions can be nice but they end up costing way more than they are worth. 2. Do not buy a fixed gear bike from walmart, target or any other big box store. These will not be enjoyable to ride and will ultimately be a waste of money. 3. Do not buy a cheap fixed gear bike off the internet such as a purefix or big shot. These bikes are only marginally better than the walmart bikes and ultimately are depending on you to spend money on fancy colors rather than quality. Some of them such as State bicycle have been improving and some more expensive brands such as Wabi are awesome but don't simply buy a bike for looks.
As far as convincing, here is my only reason for riding fixed: I like the sensation of making myself go fast. You will go faster if you ride a geared bike (or a motorcycle) but there is no other sport where I have felt as much of a connection between the physical effort and real speed. The closest other sport that I have found that comes to it is speed skating. Everything else is either too slow (running, x-country skiing) or the effort is too disconnected from the speed (downhill skiing, road biking).
There are other advantages such as reduced maintenance and such but they are not what gets me excited and from a practical perspective there isn't really much good about having a fixed gear bike. If you are looking at cars and you want to know why you should buy a miata as opposed to a volvo, you should probably get the volvo.