What type of cable can give the highest data transfer rate for an iPhone 5s?
The iPhone 5S offers USB 2.0 over its Lightning connector (USB 2.0 high speed maxes out at 480 Mbit/s ~ 0.5 Gb/s).
You will need either a USB-A to Lightning cable or a USB-C to Lightning cable. Combined with your current Mac Mini, either will give you the highest data transfer rate possible with the iPhone 5S.