Welcome!
Keep in mind that shinier does not mean sharper, and though it may be pretty, you may actually end up with a knife that has to be used a certain way or else doesn't cut as well.
This is of course if you are talking about polishing the edge bevel, and polishing all the way to the edge.
If you decide you want to try the shiny edge thing, I'd suggest the Sigma II 10k(its shiny and works fast enough to help remove all the previous scratches) and then progress through a series of strops loaded with sharpening compounds, 2 micron, then 1 micron, then .5 micron(then maybe .25 if you feel like it). You will get an edge with a finish so shiny you can use it as a mirror while you shave with it.
You may end up deciding, as I did, that this is not a good way to sharpen a kitchen knife. But it certainly can be fun, and its plenty educational.
*edit* If you really want to make life easier and shinier, the Shapton Pro 5k leaves a really shiny edge for a 5k and cuts very fast. That before the Sigma II 10k sounds like an overpowered combo for shiny. This is making me want to go play with my stones.
Keep in mind this is not an endorsement of shiny edges. Just an endorsement of blowing entire evenings rubbing knives on rocks for the hell of it.