Pinion doesn't come up in bike conversations. The term cog typically refers to the toothed rings on the rear hub. Although similar, the toothed rings on the cranks are typically called chainrings. So in a fixed or singlespeed setup, you have to decide what combination of chainring and rear cog is best for the type of riding you do. A good starting point is a 2:1 ratio where a front ring might be 32 teeth and the rear cog 16. That's what I run on my SS mountainbike. Your gear ratio will depend upon where you live and ride. Hillier paths demand lower gearing, but if you mainly ride on flat terrain, a higher gear will be OK.
I suggest you search Sheldon Brown's website referenced above and read up on singlespeed and fixed gear details. A wealth of info can be had there. He also has a gear ratio calculator and recommendations for starting points. As you ride, you'll undoubtedly tweak your selections.
BTW, you'll get all sorts of opinions regarding hubs. Nothing wrong with coaster brake hubs, but some disparage them. Even Mr. brown had concerns about them. But in my opinion, make certain that whatever you do, at least have a front brake, even riding fixed.