Building your own pc has some disadvantages. If you run into problems it will be harder to fix it. I have build hundreds pc’s over the last 20 years, mostly special systems for hospitals. If I have a computer that behaves badly I can simply change components to find the problem. If you don’t have a stock of up to date components fixing problems can be very frustrating.

I would advise you to buy a computer from a local pc shop that assembles themselves and have a good reputation for service. They can give you advise for the components. This may be a little more expensive than Dell or other cheap brands, but service is important

Just a keyboard, video and mouse is a very thin client.
It is called KVM, but since it has no pc it can only work with the pc it is attached to.

There are KWM extenders over Ethernet which allow extension for up to 300 feet for the most expensive ones.

Windows is not a multi user system.
You can not work on both the extended KVM and the pc without getting into serous arguments with the other user.

Real clients require a terminal server and a clients with a compatible operating system. This will cost much more than an extra pc.

Rob