If you have to set a bevel on a blade, I think you should work with a 1k synthetic. Once the bevel is set, I find a coticule works fine for me and the size you mentioned is the size I prefer.
Once you are happy with the edge you have from the coticule, you can take it to the next level with chromium oxide pasted on a strop. I use a balsa wood paddle strop and it works great for not that much of an investment.
THere are a lot of very good videos out there demonstrating a variety of techniques for honing with a coticule. I found the information on the coticule.be website the most useful. gssixgun, one of the honemeisters on this forum, has many videos on the web you can learn form. Ardennes coticules also has a tutorial page with pretty simple instructions for honing a variety of edges at https://www.ardennes-coticule.be/en/tutorials.
Take your time. Get yourself a decent magnifier loupe so you can check the progress of your edge as you hone. Go slow and enjoy the zen of the honing experience. It can be very relaxing.