The cheap route is to use a USB-C Hub. I have used this one across many devices and can vouch for it.
The fancy way, you can get a USB-C Dock that is basically the same thing but is meant to be stationary, so has its own power supply and more functionality.
Both of the above options would turn your desk into a generic "Work Station" at which you could sit down with any USB-C device and connect to all your peripherals.
If you want to have both computers at the same desk always on and easily swap back and forth, you are looking for a KVM (Keyboard Video Mouse). Unfortunately, USB-C is relatively new and I do not know of any that run directly from USB-C yet available.
There are may kinds of KVMs available. Some split video cables, some split USB connections, and others that split both separately. You could convert from USB-C to USB-A and then go to one of these.
What to look for
USB-C is the connection and is part of Thunderbolt 3 but the two are not the same.
You can charge many devices through the same port you connect to the hub. The first device I listed has this functionality, known as power pass-through. Often sold with the Power Delivery (PD) mark followed by the power rating for that device.
If you are going to use one computer on each monitor and want to share a mouse and keyboard, you can use software like Synergy. It's a great software that I have used many times.
There are several very similar questions on this site and no perfect answers. It's a messy area to search for, but once you know what your looking for you can find the solution that works best for you.
Edit: Answer to comment
For keyboard and mouse, there will be absolutely no problem going to USB-A. The only problem is that you said your computer only has USB-C outputs and no video output. I would recommend going from laptop to this cheaper hub and then from this hub's HDMI and USB-A to the above linked KVM. Use the first Hub I linked in the exact same way if you also want power pass-through.