I do something similar.
I mostly use mac OS X machines, but occasionally others, & of course it's a pain using multiple input devices, & monitors.
It depends somewhat on one's monitor. The monitor I mostly use has hdmi & vga, but no DVI. I connect RPi to the hdmi input, & the 4 port KVM's vga output goes to monitor's vga input. I use the same 1920 * 1080 resolution for all my machines. If an input signal to the monitor disappears, the monitor wanders around its inputs looking for a valid signal.
I've experimented with several input combinations, & so far the best (but dearest) uses:
The bluetooth setups I tried have been the least satisfactory, as of course for a start bt support has to exist on the target machine, & AFAIAA no bt on RiscOS
The other major problem (for my setups anyway) is that bt pairs devices with the machine, whereas the Logitech unifying receiver pairs devices with its usb receiver
, which means if I'm using RPi, & occasionally just want to see eg., how far a compilation is progressing on my mac, I don't need any input at all, so I can whip out the Logitech receiver from the kvm, & pop it into the Pi then later swap back, with no adverse effects on either system
This is handy if I'm constantly testing RPI & frequently switching it off & on. Normally though the RPi is just connected to 1 of the kvm's usb outputs.
Apart from 1 distribution (TinyCore Linux) RiscOS is the only OS I've found on RPi that freely allows me to unplug & re-plug input devices & still allows them to work. Trying that on any of the other Linux's fails.
The Logitech receiver takes only 100 mA so never causes a reboot on RPi.
Interestingly the Logitech receiver can handle 6 input devices which could be very useful for RPi, saving valuable usb inputs. It is however a proprietary interface, although I believe there is a basic Linux driver somewhere which cover HID usb devices, so maybe usable on RiscOS.