I have coticules and arkansas stones of several grades; and if the budget permits a full size coticule, I highly recommend it. If a natural combination stone isn't readily available, one BBW and one Coticule are only slightly less convenient and significantly less expensive.

The BBW is a faster hone (with slurry) and around 4000 grit, excellent for moving metal but not producing shave ready edges (as far as I know, some expert may know better) ..

and the coticule generally called 8000 grit and used for the final edge smoothing and thinning. Get it.

The steps you take afterwards, stropping of whatever sort, work best on a blade already as smooth and thin as possible. Stropping can't totally cover up the character of previous honing, unless one is using abrasive pastes on the strop that act AS hones.