I'm throwing in a couple of options, the 1st I've already done and the 2nd I'm considering:
1. An all-in-one desktop. This is a monitor where all of the PC's components are inside of the monitor. It doesn't make the monitor bigger/thicker, just a lot heavier due to the components. I ran MFME on it and it responded well to the machine buttons. Colour-matchine games like Bejewelled responded well on it too, originally designed for a mouse, and it kept up with the fast pace. Sadly I lost it in 2015 and my house insurance replaced it with a normal desktop. It's still an option for me again though if I was getting another new PC.
2. Monitor overlay. Search for "touch screen overlay" and look for the right size and aspect for your monitor. They clip on and run off a USB port. My current monitor has a USB hub so I can just plug it in there for cable management. Going to look for product reviews before I take the plunge though!