I think you're confused as to what a fixed gear is. That bike you had in first grade had a coaster hub, which has a built-in freewheel. Thus you can coast. On a fixed gear, you cannot. Your legs are constantly in motion.

As for your original question, the Kilo TT is a fine choice for a first fixed gear. Just remember that their sizes tend to be a bit wonky. I can't remember what it is; if a 53 cm fit more like a 50 cm or if a 50 cm fit more like a 53.