Nah, you can probably get by cheaper. If you're only going to be using this bike fixed and it's in good running order, you can recycle the existing chain by taking out whatever you need to. Strip the crank, if you have a double the small gear is probably around 42t (middle on a triple). All you really need is the rear wheel and cog. Cheap rear ($90) + cog (just getting started a 16t is probably a good match with the 42t, $20), and lockring ($10). All told, $120 if you can recycle everything else.

(btw, the $90 is about going rate for a Suzue basic laced to a Mavic MA3--the $120 wheel 165 cited is really worth the extra $30--would bring the total cost up to $150).