Eithernet Connection

I don't really understand the question completely.

If you have Internet Service and a modem, the modem should have Ethernet and may also have Wireless. But the Wireless is internal to you (not the outside world) and should not be unreliable.

In any event, you can plug an Ethernet cable into your router and into your computer and it should work fine.

Perhaps shut down (power off), plug in the Ethernet and start up. It should work fine.

I have ethernet & have had it for years.

The wireless goes down about once a week; it comes through the cable company. They instruct me to restart the wireless router; unplug, wait 30 seconds, plug back in.

I'd prefer NOT to count on wireless for my main internet connection.

Richard

In most configurations from cable providers, the wireless router is really a part of a single device that is responsible for many different functions.  For example, Time Warner cable uses an Arris Telephony Gateway which is responsible for providing phone service (via VOIP), ethernet based internet access and wireless based internet access.John is simply instructing you to check the back of your cable providers wireless router to see if there are any ethernet ports.  If there are, then you should be able to plug your computer into any one of the identified LAN ports without issue.

-saige-

I am aware of the back of the router, ethernet ports, etc. I know how to physically do that,

My concern is, it's a BRAND new computer, Windows 10, it behaves entirely differently from anything I've ever had, so I'm being cautious.

For all intents and purposes, John is correct.  Windows 10 all the way back to Windows XP, work pretty much the same way (Windows 2000, Windows Server 2003 and Windows XP were a little more temperamental to some IP stack configuration changes, which meant they required a restart in order to implement the configuration change).

I would be remiss, however, if I were to say that their implementation under-the-hood (so to speak) was the same.  It clearly is not.  But in most scenarios, those under-the-hood implementation details do not, directly, affect the end-user.

-saige-

The wireless may take priority up the ethernet,  unplug or disable the wireless

and  just to back all suggestions : when you plug in the wired ethernet, it will normally be the preferred one  used by the PC

That's all true. But I wonder if your issues are really originating from Wireless ... It adds potential issues, in particular after wake-up of wireless connected devices, but having to reset the cable modem sounds strange.
However, it is worth a try, and nothing to loose.

If you are concerned about the security of the other computers.  Turn off the other devices, bring the new PC online, go through setup, scan with Malwarebytes, test internet speed at speedtest.net.

I think there is very little concern if it is a factory PC.  If used but new to you, you can turn others off to isolate it.

Thanks Richard and I was happy to assist.