depends on your resources, honestly. Converting an old road bike teaches you a lot about bike mechanics right off the bat, so you sort of know what you're doing. It's also pretty fun, and it's fulfilling. That being said, you need to find a frame or a bike that would be good for a conversion, (Semi-horizontal dropouts). Since fixed gear is really popular, the market for these bikes is pretty limited, so you're either going to find a ****ty bike that would make for a ****ty conversion, or a nicer road bike that wouldn't be worth converting.
That being said, there's nothing wrong with getting an off-the-shelf fixed gear/track bike. Kilo's are great beginning bikes, and as you replace components as you need to, you'll learn about mechanics and components.