You can connect a Windows computer to a Raspberry Pi over the internet. You only need to use a serial connection if you are connecting from an Apple II.
Method: on the PI, create a new user, say “wilkiecat”, and give this new user a password. Then type
sudo raspi-config, and start the SSH server.
On your Windows machine, download “Putty”, choose SSH and enter
If your cat is called “Wilkie”, and your “Pi” is called “wilkiepi”.
If you downloaded and installed “Raspple”, it will automatically install the avahi daemon which allows you to call your Pi by its name instead of the IP address.
If avahi daemon is not installed on your Pi, install it now by typing:
sudo apt-get install avahi-daemon
Well after connecting to your PI, you will see in the “Putty” window: