You have been given tons of great advice so far..... don't ya love the gang here !
Here is my .02 cents.... Number one the KME knife sharpener is the greatest tool ever devised hands down on this planet ! Number two I have a complete set of diamonds, ceramic, and arkansas stones thanks to Ron and IMHO the xtra coarse diamond and medium arkansas are the best two stones to have, then strop on leather. The number one issue some folks have that are new to a KME is getting the bevel set on a blade ALL the way down to the edge and forming a burr FIRST. Once that is done then you can polish an edge to your heart's content going thru as many grits as you prefer. I just cannot say enough good about a KME.
On all my kitchen knives I simply use the X coarse diamond and sharpen to a burr, flip and sharpen to a burr on that side, then flip back and forth a few times lightly taking the burr off and good enough for a month of kitchen duties usually. Dishwasher, banging around on each other in the drawer, and a wife and daughter who like to cut cornbread with them instead of a steak knife right on a hard plate.... well you get the picture. Hell on a nice KME edge so I do not spend lots of time on them getting them to a polished razor's edge.
On my broadheads or hunting knives I do go from X coarse diamond to a med arkansas, then fine, then leather. Makes a huge diff and as others have said above, " gets rid of the toothy edge", that you get from the x coarse diamond. However, even though your edge may not feel as "sharp" and grabby, rest assured it is and will last longer and cut you before you know it ! Nothing like a true razor edge. We normally gut 4-6 deer a year off a KME razor edged Buck 110 folder that you can buy at Walmart for $30-40. You can still shave with it and we gut our deer all the way to the brisket, cutting thru the cartilage that connects the ribs to the sternum too. I can only imagine what a great knife would do with a KME edge. Before KME I always loathed trying to sharpen a Buck or Case knife due to their high hardness and not being able to hold and keep a consistent bevel. Now that hardness only means a longer lasting edge thanks to a KME. JMHO fellas.......