I think the most valuable thing to me about starting on a conversion was the learning experience as far as getting to know a fixed gear bike bike, using the proper tools, etc.
I converted on old road bike on the cheap with a rear wheel at first, then eventually got cranks and a front wheel and was satisfied for about a year before upgrading to my IRO Mark V Pro (after the road frame was damaged in a car accident).
If I had bought a kilo tt or similar to begin with it might have taken me longer and cost me more money on swapping out parts I might have thought needed replacing to reach a certain level of comfort maintaining/appreciating a bike.
Just sayin'.