This week's book giveaways are in the Jython/Python and Object-Oriented programming forums. We're giving away four copies each of Machine Learning for Business: Using Amazon SageMaker and Jupyter and Object Design Style Guide and have the authors on-line! See this thread and this one for details.
You should probably define what you mean by "connect", as the answers will vary depending on what level of connectivity you want.
Most modern Macs (the Minis included) come with OSX installed - a BSD Unix based system. As such it could act as the server to your work on the PC laptop. All you will need is Ethernet connectivity between them.
You can utilize a KVM switch to connect one Keyboard Video & Mouse to multiple computers. The Mac Mini uses USB connections for keyboard and mouse, so depending on what you want to use, you may either need a KVM that understands USB, or you may need a USB to PS2 adapter. I have found the later to be a little flaky if you try to hot-plug them in Mac Minis (simple solution: don't hot plug them ).
If you are willing to have a monitor dedicated to each machine, then you might want to look at something like synergy, which allows one system to host the keyboard and mouse, and multiple other systems to share them. Whichever screen you move the mouse into takes keyboard and mouse inputs. In my opinion this is nicer than a KVM since you have the 2 screens visible simultaneously, but obviously it requires you to have 2 screens and the desk space for them, plus an ethernet connection between the 2 computers, and possibly a keyboard plugged into the slave machine to start up synergy (although you can get around this by having auto-login and auto-startup of synergy on login).