I would use a medium stone and an inexpensive buffer to chase the lines from the medium stone, remove the burr and create a strong but thin apex.
that's probably something like $100 total. I'm sure there are people who have had more stones than I've had, but not many. I've had maybe 500 and still have somewhere between 100 and 200.
The reason I mention the buffer is that it's very good at finishing the edge of a tool even if the hardness isn't very high, and he buffing of the tip of the apex leaves an edge that's more durable....even again, if the hardness isn't that great. Higher hardness steel generally finishes pretty easily off of anything, especially if it's plain, but most of the knives that people bring me aren't very hard and the top end of the range seems to be like henckels or wusthof, and both are still not that hard - especially newer versions that have been cut back to be steelable. I'm not a professional sharpener, just relaying what I've seen. After buffing the apex of a knife, I usually steel it to knock a bit of it off as it's too sharp for the average person who doesn't use a sharp knife.