The Chef's Choice 120 sharpens 20* angles and is not appropriate for your new Japanese knives. Chef's Choice makes three different 15* sharpeners and one which sharpens at both 15* and 20*. All four of those are appropriate. Of the four, the model 15XV is the best. If you're still interested in a Chef's Choice electric sharpener, we can compare and contrast all four.
CCs have strengths and weaknesses. On the negative side:
- They don't perform well when they get dirty and "load up," and are not easy to clean; and
- They aren't particularly versatile -- each machine will only sharpen one type of angle and one type of geometry.
- They are fast;
- They don't have much if any learning curve;
- They are convenient enough to get used whenever needed; and
- Unlike many old-fashioned electric sharpeners, they won't hurt your knives if you use them correctly. There are a lot of bad electrics, and a few good ones. CCs are among the good ones.
The bottom line on CCs is that compared to a skilled hand sharpener, or a good tool and jig system, you give up some versatility and ultimate edge quality in exchange for ease of use and convenience.
From your description of what you're experiencing with your 120, I'm guessing that it's dirty and needs the plates cleaned or replaced. I suggest contacting the manufacturer, EdgeCraft, and asking for support.
An alternative to the CCs with a similar set of strengths and weaknesses is the Minosharp Plus3.
If you're only going to use the DMT XXC for flattening and not for repair or profiling it's overkill. The CKtG 140 diamond plate does as good a job of flattening for a third the money.
There's nothing wrong with your proposed two-stone kit; but nothing particularly right about it either. It's a sort of strange choice for a beginner. What led you to it?
If you're priorities lie more towards "really good," than "really inexpensive," I suggest CKtG's three-stone, eight piece kit.
Don't expect to buy a couple of bench stones and start producing great edges on the first day. In my experience it takes beginners somewhere between 10 and 20 hours of practice to produce good edges consistently. The most reasonably priced alternative is a good tool and jig system like the Edge Pro or Wicked Edge. The EP takes around 2 hours of practice; the WE takes even less. Take a look at CKtG's Edge Pro Essentials Kit.
I've been freehand sharpening for around fifty years. My generic advice for those who don't know how to sharpen yet and don't need the versatility of bench stones is to buy an EP or WE.
All knives are subject to bending burrs caused by impact, aka impact burring
. That means the get tiny bends on the edge when they bump into something hard -- like a bone or a cutting board. When the edges bent they need to be trued. There are a few ways to true. You can use a honing rod, aka "steel;" "touch up" on a stone; strop on whatever; run the edge between flexible wheels (as on some CCs); etc. Not all knives are good candidates for steeling. Some are too brittle, too hard, too asymmetric, sharpened too acutely, and so on.
Even though the Tojiro DP is a bit brittle, it's still well within the envelope where steeling is a good choice. You can use an Idahone rod (great rod for a great price) on a Tojiro DP, but you have to use the rod so as not to chip the knife's edge. That means appropriate angles, very few strokes, and a very gentle touch. Read my article, Steeling Away