Starting out with nothing but a coticule in my opinion is setting yourself up for a longer, harder uphill battle than learning to hone needs to be. Coticule have a range of performance and characteristics, no two are the same thus yours may vary greatly from mine. I can use mine as a mid range stone, or I can use it to finish. But it can't do both at once as it had to be burnished and used with oil to become a finisher.

I would echo the advice of others. Norton, Shapton, Naniwa, or King stones at least to 8k. Most folks can shave comfortably at the 8k level so that's a good place to start and you can always expand the line upward later when the mood/need strikes you.

I started with a set of Nortons and a Cnat. The only thing I would do different starting over is focus on the 1/4/8 synthetics sooner and shelving the natural until I knew how to use the synthetics better.