Think the mac mini has to be wired into your system (at least your display), so having it with you isn't really feasible.
For the laptops, the theory is that the airport can be used to stream to a DAC, so you would have the airport next to your stereo, plugged into a wall wart and your DAC via coax. The laptop would stream data to the AP wirelessly. Cannot comment on that one, because I've never tried it, but I'm pretty confident on the set up.
The strange part of the laptop thing that I've never liked is that if you run it in conjunction with a NAS (network attached storage), presumably the laptop has to pull data off the network via 802.11, process it, and then push it back out to the airport for routing to the DAC. Seems like the data has to go both to and from the computer via wireless for that to work, and I don't know whether there is enuf bandwidth. Of course, you can always maintain the library on the notebook. I've never wanted to do that b/c I've got too many files. YMMV.
The squeezebox is a thin-client. You hook a squeezebox up to a network (wireless or wirelessly) and also to your DAC. The squeezebox interacts with an application running on another computer on the network (in background mode, generally), which "pushes" data out to the squeezebox based on input from the IR remote that talks to the squeezebox.
