Can't speak for the 500C, but most of the systems and the wiring is the same across cars, find a suitable stereo, I would advise going for a a known brand, Alpine, Sony, Pioneer etc. Rather than some of the Aliexpress Android units.
You'll need a fitting kit, which normally includes a wiring harness, stereo fascia plate/adapter, interdace for steering wheel controls, tools to remove the current stereo and an aerial adapter.
You may also need an aerial amplifier as a lot of these cars have the amplifier in the old head unit, but this is only an issue if you use AM/FM.
You may also need to run a new microphone, GPS antenna and DSB antenna if included with your new stereo - these are normally the worst bits of the job.
Check out dymanic sounds who offer fitting kits and all the bits you'll be likely to need.