Welcome back to the Amiga community and to the best group of Amiga users on the planet!
You did not list any graphics card with your A1200 setup, so I must assume that you are limited to 15kHz horizontal display output. Unless you have a Multi-Sync monitor that can display 15kHz and standard VGA display frequencies, it is not going to be possible to use only one monitor (but you probably already know that). So, you need a Scan Doubler/Flicker Fixer, or the Multi-Sync monitor and then you can just get yourself a 15 pin switch box to go from displaying the Amiga's output to the PC's display output and back again. Keyboards and mice are a bit more complicated and I am looking for the same solutions myself. I have an adapter that allows PC mice to work on the Amiga, but have not tried it through a switch yet. There are also adapters that allow PC keyboards to be used on an Amiga (I think, if not someone here will correct me).
I have just cleared the wall space in one of my rooms and have drawn the desk/racking system to hold 7 of my Amigas and my monster Dell tower, with 2 - 20" TIMMs and 4 - 1084s connected to 2 A4000 Toaster/Flyer systems, the Dell 20" widescreen, a Nokia 15" connected to the A3000T, and finally 2 last 1084s connected to switches to display the outputs from 2 A3000Ds and 2A2000s. The goal is to network all 8 computers together to speed Lightwave rendering, as the slowest of the group are the A3000Ds w/WarpEngine 040/40mHz in them. (for other members here - no need to tell me to give up using Lightwave on the Amiga and switch to the PC, it will happen when it happens, let me use what I have for a while longer)
Good luck with clearing your desktop, and let us know what you find that works.