I built my first fixed gear about 10 years ago, cobbled together from the parts bin on a Peugeot frame.

I built my second about six years ago on a Shogun 400 frame recovered from the local dump, but it still cost me over $400 for the new parts. That bike is a joy to ride. It's first major outing was the Paris-Brest-Paris 1200 in 2007, and although I DNFed, it wasn't down to the bike. I toured on it through France and Belgium and England afterwards, and did a full year of century-a-month on it.

I had a 39-17 set-up on it, but most recently have gone to 39-16, and I can tell you that the one-tooth change in the cog is significant. I haven't been riding it as regularly as I would like, but the ride is nice and I enjoy the bike immensely.

If you want to go in steps, and the rear hub currently has a screw-on freewheel, then (a) remove the freewheel, (b) get a cheap BMX single-speed freewheel in, say, 17 teeth, (c) put that on the hub, (d) remove the derailleur, (e) shorten the chain and keep it on the 39T ring (assuming you have that size), (f) adjust the chain tension in the horizontal dropouts... and (g) go ride. You have a single-speed so you can get used to the gearing.

When you feel ready for a fixed gear, have the bike shop remove the BMX freewheel, put on a FG cog with lock ring and you then have a fixed gear. It's best to get the bike shop to do this initially, as they will have the tools to get the lock ring done up tightly to avoid the cog from coming undone.

To entirely overcome this issue of the cog coming undone (most likely will occur if you attempt to back pedal or use the pedals to slow down), you will need a new special hub laced into the wheel. As chasm says, you can get a flip-flop hub that gives you a single-speed OR a fixed gear option on the same hub.