At the moment I’m using a Canon 100D. Will the Phottix Ares II transmitter and receiver work with a Yongnuo YN-560 III speedlite?
If you attach the transmitter to your camera's hotshoe and the receiver to the foot of the flash, they will work to trigger the flash off-camera. But you cannot use TTL, HSS, 2nd curtain, or control the power level of the flash from the transmitter. The Ares II are manual-only triggers. The Strobist recommends them for pro-level reliability, not for features. But if you're a hobbyist, maybe you'd prefer more features over reliability for your buck, since heavy-use reliability may never be required with only occasional light usage.
A possible better choice would be to get a Yongnuo YN-560-TX transmitter. This will work with the radio receiver that's built in to a YN-560 III, and will also allow you to remotely control the power level of the flash.
If you don't yet own the Yongnuo YN-560 III/IV/-660/-720, an even better choice for a low-cost manual off-camera flash combo might be to get a Godox TT600 and a Godox XPro-C (or X1T-C) transmitter, which will get you remote power control and HSS. Well, at least at the time I'm writing this (summer 2018). Tech moves fast in the cheap Chinese flash world.