Hi pa42. Forgive the delay; I was away vacationing.

I'm a bit familiar with what you're asking for. ;-)
Yep, there are softwares that allow you to capture images from your digital camera remotely using your laptop or desktop computer. One I use is Nikon Capture 3 Camera Control. It allows me to operate my dSLR via a computer hookup. The images are viewed on the computer monitor (rather than on the dSLR's LCD) and the shutter and camera settings are operated from the keyboard. The two are cabled together.
I've used this approach to capture images through a microscope. It's also often used in studio work, and other applications where you want a large viewable image and access to immediate storage on a harddrive, etc. I've even seen a pet photographer use this setup to photograph pups with Santa for the holidays.

Canon cameras and Nikon cameras have a remote capture software available. I'll bet other brands like Fuji have something available too.
As for what type of computer, you can use an Apple platform or a Windows platform computer in either a desktop or laptop size. The specific requirements (processor speed, ram, etc.) would be indicated on the software.
Hope this helps.
Cheers,
Deb