A modern Mac mini has multiple connections that can be used for an external hard drive, including USB 3, FireWire 800, and Thunderbolt. They are all excellent options, although Thunderbolt has the highest theoretical throughput, although all will exceed the maximum sustained throughput from an external hard drive. You can even use the ethernet port if connecting to an NAS, and that should work adequately for audio applications. So your answer for the best choice for the Mac to hard drive connection is likely any of the above options.
As for your observation that networking affects audio performance on the PC (interesting), not all network interface cards are created equal. The better ones offload much of the processing from the computer's main processor and does more of the work on the card itself. This may affect processor availability for audio applications. I also find it better to use dedicated (external) router/firewall appliances rather than running such software on a general-purpose computer.
Michael
As for your observation that networking affects audio performance on the PC (interesting), not all network interface cards are created equal. The better ones offload much of the processing from the computer's main processor and does more of the work on the card itself. This may affect processor availability for audio applications. I also find it better to use dedicated (external) router/firewall appliances rather than running such software on a general-purpose computer.
Michael