When stripping wire, the flat side of the strippers should face the end of the wire. When the beveled side faces the end, pulling the tool will compress the insulation you are trying to remove. Also, after you have firmly squeezed the stripper (manual type) release the pressure a little and pull the insulation off. Rotating the stripper, increases the chance that you will cutoff a few strands, thereby reducing the wire size. Another trick I use is to grab the insulation beyond the strip point with the stripper jaws and use that to pull the insulation off the wire. These prevents the breaking of any strands as the sharp edge of the tool pulls across the strands. I like the automatic type you show. These are available at most home stores and Radio Shack. They are all the same tool but the price varies widely ($10-$25).
As discussed, never, ever tin wires for use in the WAGO connectors. They are designed to compress stranded wire for maximum current (highest contact area=lowest series resistance.) and when stripped the proper length (5/8") will achieve the greatest pullout force. WAGO does make a terminal for solid wire, the PD does not use that type.
Alan, we use non-insulated crimp connectors and solder each one, covering the terminal with heatshrink. It is just extra insurance.
I find that slightly tinning the wires to be spliced actually aids in the process. The wire becomes a little more stiff and some solder is already on the joint before you start the soldering process. This also prevents strands from sticking out and puncturing the heatshrink later. Remember that if solder does not start to melt, it may mean you do not have enough heat transfer. Add a little more solder to the tip of the iron and heat the joint again. A good solder joint will have a nice shiny appearance. If you add too much solder, the solder will wick up under the wire insulation making the wire very stiff up to an inch or more from the joint.
No matter the connection (solder, crimp, screw down, or WAGO), always perform a tug test. If you can pull it apart, you need to start over.