Alright, there are a couple of things to get set up on the main box as well so we can work with our SepplesberryPi w/o having to use either a monitor, keyboard, or mouse connected to it. We'll connect it directly to our main box with an Ethernet cable for it's networking. IIRC, I think W*ndows calls this Internet Connection Sharing, but ofc we'll be using Linux instead.
So, I use the WiFi for my main box's Internet access. This leaves the Ethernet wired port available. And it's this port we'll set up for the RPi to get out to the network with. You configure the settings on your main box to bridge the two connections (and this will also provide DHCP settings for any incoming clients connecting through the Ethernet port). For the RPi, you don't have to do anything special, it just werks.
BTW, YMMV. This setup is workable for my specific situation. You may want to connect yours straight into your router, or across the WiFi, etc. Just make sure you can figure out what it's IP address is afterwards b/c you'll need it for the other step.
Then, we'll use VNC to control our RPi remotely. The RPi has the VNC server software already installed, but we'll need to install the viewer software on our main box. Once everything's set up, you'll no longer need to use those other peripherals to work on your RPi dev box.
Go ahead and plug the two boxes together with the Ethernet cable in between.
On your main machine, choose 'Advanced Network Configuration'.
Select the Ethernet connection, then click the little gear for 'Edit the selected connection'.
Choose IPv4 Settings > Method > Shared to other computers then save.
That should be all that's needed. Power cycle your RPi and it should now have an IP address given to it by your main box, and should be able to get out to the Internet as normal also. If things don't quite work for you at first, you might check the ip addresses on your main box with ifconfig, and also try pinging some known-good domain to make sure there's not any issues with the main box itself. As always, you can ask questions ITT.