madera, I'm glad to see you intend to get some sharpening stones. My first recommendation is that you do not get any stones which are smaller than 200 mm X 50 mm. And larger than that is better still.
A good place to start is to read this post by Chad Ward on how to sharpen: https://forums.egullet.org/topic/26036-knife-maintenance-and-sharpening/
And some of the best videos showing how to sharpen are done by Jon Broida, here: https://www.youtube.com/user/JKnifeImports
I read from your posts that how the knife looks is an important issue with you. However, please be advised that I have a different view. I believe that how well the knife works is the overriding most important factor, followed by cost, and how the knife looks is a distant third.
In fact, some of my most cherished knives are referred to as “dirty old carbon” knives – well used, but cared for, with stains and other blemishes in appearance that reflect proper care during that usage.
In fact, for any carbon blade, it's been my practice to induce a deliberate patina, so that the surface of the steel will be stabilized and passivated against further oxidation.
Black or dark brownish colors are good and are a strong indication of Fe3O4. That's what forms with proper development of a patina. Red or orange is Fe2O3 and is definitely not good – that's rust and needs to be scrubbed off as quickly as possible.
I recently acquired a CarboNext 240 mm gyuto, so I can probably recommend against your acquisition of the knife. The reason isn't the potential for staining – it's because the knife comes somewhat crudely finished along the edge. That is perfectly normal for many Japanese knives sold in Japan to Japanese chefs. Japanese chefs are trained to properly finish the edge of a knife, so as to place an edge that they individually want on a particular knife. Westerners, on the other hand, expect that the edge put on at the factory is the best. Different cultures, different expectations.
For the size of the knife, I would recommend getting a 240 mm blade. You will be using it enough to make the length and width of the blade a significant difference.
I am assuming that you are using the word thickness to refer to the thickness of the metal at the spine. Certainly, thickness makes a difference as to the stiffness of the blade. But how well the blade thickness tapers down to the edge from the spine can be important. What others refer to as “thinning the blade behind the edge” refers to a selective thinning by a very experienced sharpener using a bench waterstone and hand sharpening, so as to thin the overall thickness of the blade very near the edge. That helps tremendously in cutting down on the “wedging” of the blade when cutting through foods.
As for your using a professional sharpener's services, before committing and putting your blade in that other person's care, ask how the knife will be sharpened. If you are shown stones – that's very good. But if you are shown a motorized sharpening machine, do not have your knife sharpened on it!
As for the thinness of the FKM, it's not unusual for a shorter knife to be thinner. Longer knives need to be thicker to compensate for the additional leveraged force that the longer blade will place on the metal.
Now for a specific knife recommendation.
You might want to consider a MAC “Chef Series” BK-100. I use one as my principal blade.
On the negative side, it's really a very un-fancy blade. There's no bolster – just plain riveted scales. It's also not promoted very much. Most who buy it seem to be professional cooks just starting out. And if appearance is important, it's probably not what you would like.
But, it's a MAC chef's knife. The steel used is exactly as is used by the MAC Professional MBK-95. And I can tell you from personal comparison with the MBK-95 (I own a number of MAC knives), that both knives have the same thickness (2.5 mm) and the same level of stiffness.
Since you are in Germany, you would be buying from the German importer, kuechenmesser.de. The BK-100 price is €115. The web page is: http://www.kuechenmesser.de/shop/index.php/language/de/cat/c19_Chef-Serie.html
If you are travelling to the United States, and if you have access to an American shipping address, then you can order a MAC BK-100 from Chef Knives To Go for about $110, shipping included (but not available to be shipped outside the United States). The web page is http://www.chefknivestogo.com/macchse10chk.html
You should also acquire a ceramic honing rod. The 12 inch (300 mm) Idahone fine grit rod is what I use. Do be advised that a ceramic rod will shatter if it is dropped.
For some valuable tips about honing rods in general, read here: http://www.cookfoodgood.com/?p=551
Hope that helps.