I think the s8+ can support both USB-pd and quick charge (someone who owns one may know more).
The powercore redux and lite do not support either standard so will only charge at standard USB speeds.
Both powercore II models will provide a quick charge using poweriq 2. Charging your phone will use a USB a to c cable and charging the power bank will take a micro USB cable.
The powercore pd uses USB power delivery and will charge your phone at 5v 3a with a USB c to c cable and the same cable will charge the power bank.
In this case I would recommend the pd because although it charges at 15w vs the 18w off quick charge (is this right?) you will be able to charge your phone and power bank with a single cable. It may not matter, however, if you are going to carry a micro USB for your MP3 player.
Source for info: https://www.reddit.com/r/GalaxyS8/comments/69xox4/the_galaxy_s8_supports_usbpd_5v3a/