I use the Chosera 1K and 5K stones for most of my sharpening. I'm trying to choose between the Chosera 10K and the Nubatama Bamboo 15K (or 10K) as a finishing/polishing stone mainly for polishing/finishing the secondary edge. I've tried the Naniwa Superstone 10K and thought it's too soft.
ARNIE <> In the abstract - as this is a pretty vague question, Choseras are top tier stones that are hard to dislike. Naniwa 8k Snow Whites are lauded for their polish. Kitayama's are appreciated for their range as their mud refines exceptionally well (8k-12k). I have a Nubatama Bamboo, albeit 1200, and love the feedback, love the mud, cuts consistently, wears well. I think the 10k is a better option for you as the 15k seems like a bit of a jump from 5k; you're just rounding 5k teeth at that point - not truly refining the edge by replacing the 5k scratch pattern. Then there are the Shaptons. I just started using the Pros, and they are really nice stones. The Shapton Pro 8k is another option for you.
+1 on the naturals. I just spent some time with Ken discussing naturals yesterday and there is simply something special about a chunk that has been pulled out of a mountain and is unique . . . not to mention that the polish they give is, um natural .
I had one small natural stone and now I am going further down that route. The natural stones were not all super expensive either. Since you already have synthetic in that grit range and at a price point that includes naturals, why not try something different (there are several very hard natural stones in this range)?
ARNIE <> With this line of thought, I recommend a Yaginoshima. I pretty much finish all my knives on it, that I want to bring to that high level of polish, at least. http://www.chefknivestogo.com/yaas.html
Knives - Right now, I have a Carter Funayuki (white steel laminated with stainless), a Takeda Nakiri, a set of Shun steak knives, and a older Henckels stainless carving knife, and a few older cheap stainless knives to learn and practice on. I've also thinned and reset the bevel to about 15 degrees on the Henkel.
Next purchase will be a petty knife. My small collection is quite varied, but I'm liking the Japanese knives and carbon steel better than Western handles and stainless, so future purchases will likely be carbon steel and not stainless
Stones and sharpening - I've been practicing hand sharpening on stones a few times per week, and think I'm getting the hang of it. I started out with King 1K and 6K stones. I didn't like the 6 K stone, so I picked up a Takenoko 6K stone. I also picked up a 600 grit Chosera when I wanted to set a new bevel and thin out the Henkel. I really liked the way that stone felt, so I also bought a 1K and 5K Chosera (which is what I'm mainly using). I wanted a higher grit polishing stone, so I bought a 10K Naniwa Superstone, but don't really like it as I found it to be too soft (at least for where my technique is at now).
Here's the video of the Yaginoshima Asagi using a tomonagura to enhance mud formation:
While the 15k Bamboo is a truly exceptional stone, you should focus on getting something in a 10k range first if you are going towards synthetics. The 10k Superstone is quite soft, so you might want something like the 10k Nubatama, Chocera For 8k and 15k stones that's yet another topic. It's not that the 10k SS is a bad stone ,just that some like softer and some like harder stones. This is both a matter of personal preference and a variance in what most consider ideal for specific tasks.
ARNIE <> Whereas Boar's point is poignant, you will never find one stone that is best for every situation; I stand by my Yaginoshima recommendation as a great choice for a broad swath of situations.
While we're on this specific tangent of Japanese Natural polishing stones, I will disclose I only have & have used two, the Yaginoshima & the Ozuku Asagi. The Ozuku is crazy hard & I reserve it for my razors, but I have used it on my Kata-ha knives and for me, it has refined those carbon yanagi & deba to levels in which I find too sharp for service. The Yaginoshima has replaced my Kitayama as my high grit finishing stone on knives in which I wish to bring to that level of polish, as I stated earlier. I do not bring my pettys there, but I do bring my Gyutos/Sujis/Debas/Yanis there. The Yaginoshima has created edges on my high Hrc stainless, semi-stainless, & carbon edges that have uniquely bridged that gap between bite & clean cutting. It creates a beautiful Kasumi on clad knives. For me, it has simply been a wonderful one stone go-to finisher. I would love to have the finances to test any of the Ohira variations, Hideri Namitos, Nakayamas, and whatever other cool stuff Ken is hiding, but I bought one & have been thoroughly impressed & pleased with how well it has performed in a plethora of applications.