Correct pretty much:
Incoming, I assume fiber or coax to your service provider MODEM. Please use the provided RG-6 COAX as it will be double shielded and meet FCC emissions requirements. At this level, bits are bits.
Modem to a router with Ethernet cable:
Most use the provider router. Provider Routers are fine for wired, but WIFI performance is often very poor as far as bandwidth and range. Not a problem for most uses but if you have range issues or hard core gamers, you may want to look into higher performance routers. Irrelevant for audio quality as it is still a packet based data delivery service and bits are still just bits at this level. The data rate is trivial. You can cable Ethernet or consider WIFI to the computer or streamer. I prefer to cable anything that does not move, but WIFI can carry HD stereo bandwidth just fine. Still packet based delivery. Bits is bits at this point. TCP will correct any errors. If running UDP, shame on you but the higher levels of the stack may still correct any error.
Again, a shielded Ethernet cable does NOTHING unless the ports on both ends are plated to provide the shield ground. An Ethernet cable does not have a pin for shield. Why? Because it is not necessary. There are some applications in the Medical field where emissions could cause errors in other equipment so shielded cables are required. These locations usually specify isolated power grounds. It is not a good thing for your IV pump to glitch. You can buy consumer level routers, switched, and hubs with plated connectors if you believe you need it.
CAT5+ had the sole advantage of bonding the pairs for more consistent impedance when going to Gig-E. CAT-3 is all you need for audio bandwidth.
If anyone would like a better factual understanding, might I suggest, rather than believing some You-Tuber or subjective reviewer sponsored by snake oil manufactures, ( or me) you review a little more reliable information. Here is a good place to start on WIKI.
https://en.wikipedia.org/wiki/Ethernet
If you want to dig deeper, MIT has their entire engineering course selection on-line for free.
A streamer is nothing but a stripped down computer loosing all the services not needed. They attempt to make a computer an appliance as they should be. I use a PC as a music server and for the limited streaming I do as I like the bigger screen for my UI and don't own a tablet. It has about half as many services running as an out-of-the -box PC and many configuration changes. Audio quality was in fact improved by PC and Music server application configuration for how the processing of those bits was done to assemble the USB output. Stream or disk file. Bits are still bits, but different bits. Subjective reviewers suggest a Mac is a better platform but I don't own one so I do not know or if using ASIO or WASAPI has the same advantages as the Apple music stack. A streamer appliance should have these taken care of these questions so you don't need to understand them.
Eventually, those bits get delivered to a DAC. Internal or external. How the DAC input DSP processor handles them and how they are clocked does seem to make quite a bit difference in sound. Some well understood and measurable, some maybe not fully understood. Next D 2 A conversion. That is the easy part. This is followed by the integrator and analog stages. There is gets harder again and can influence the quality. Much understood, some not, and tons more opportunity for snake oil salesmen. ( Did you know you can bias an op-amp into class A?)
Now, to confuse things further, Ethernet CABLE can be used for other transports. I used a CAT-5 run between baluns to send low quality background music from my cable provided audio ( before I canceled cable). I did not have any noise issues, but as it was audio over the cable, it was subjected to degradation though the baluns probably did more harm. Ethernet cable is used for proprietary links in automation and I believe in professional audio production. I do not know anything about that other than the cable is cheap and the connectors are excellent.