Recommend me a KVM switch

My home desk has a lovely mechanical keyboard and shiny big monitor on one side, and a crummy dome Dell keyboard, and old-ass crummy monitor on the other to hook my work laptop into for a dual-screen work setup (the two screens being the crummy monitor and the laptop screen itself).

I'd like to move over to a KVM setup with a one-touch button to switch between the two, so I can clean up a lot of desk real-estate by dumping the crummy monitor and horrible K+M.

Looking for one that supports DisplayPort and a 1440p resolution (for the home computer), and an HDMI connection on the work computer (1080p would be fine for that) - though I suspect the simplest solution there is a Displayport KVM switch and an HDMI-to-Displayport cable.

Further complications: I'm rocking a Corsair K95 keyboard too, and some of the KVMs I was looking at specifically say they don't support "gaming keyboards". Given that the home computer is my gaming rig, minimal lag is important too.

Any recommendations?