Not an expert, but I have done a bit of checkering. Depending on how bad it is, I normally use a "riffling file" for light clean up, or a single line tool followed up with the riffling file. I would recommend getting the short reverse cut tool as well for your edges if you haven't done much checkering. I also have a riffling file that I snapped the point off, and it works very well for getting up to your borders without cutting over them.
If you are using a single cutter tool, spacing per inch should't matter, but be aware there are 60 degree checkers and 90 degree cutter (the angle between the diamonds) I use 60 deg, and they should clean up a factory checkering job. If you want to cut more than one line at a time, than yes spacing will matter. You don't "need" a complete kit, but if you ever want to checker from scratch, you will need the whole kit...... Hope that helps.
