I've done a lot of this type of thing.
Gigabit Ethernet is by far the fastest method for copying files among those two computers. Just set up file sharing between the two computers (
https://support.apple.com/en-us/HT204445), and hook them up with an Ethernet cable (assuming they aren't already wired to the same network).
If you don't have an Ethernet cable, then second fastest would be Firewire 800 via Target Disk Mode as others have suggested.
If you don't have an Ethernet nor a Firewire 800 cable, then third best would probably be file sharing over Wi-Fi
if you have an 802.11N wireless router
and a decent connection to both computers.
Probably dead last would be copying it from the laptop to an external drive, and then copying it all again from the external drive to the Mini. I've had to do that a couple of times, and it's something you set up to do overnight.
I've also noticed a substantial difference between, say, a files that add up to 500GB vs thousands of files that add up to the same size. Even though it's the same size, transferring that many files can take several times as long as just a few files of the same total size. I'm not familiar with iPhoto library file structure, but if it's thousands of files, I'd ZIP the whole thing first and transfer the ZIP file. Especially over a slow connection, this could save
hours.
