Type-C Non-Negotiated Power and 20V protection
USB charging has become very complex but also very powerful. There are several official and de-facto standards used concurrently:

USB 1.0 / 2.0 / 3.0
Apple chargers
Qualcomm Quick Charge 1.0 / 2.0 / 3.0 / 4.0
USB Power Delivery

All standards will initially deliver 5V (or sometimes up to 5.2V to compensate for losses in the cable).
Plain old USB charger
The plain old USB charger will deliver 5V at up to 1A. Some chargers deliver up to 2A; usually they are labelled accordingly. They all disregard the USB specification (version 1.0 / 2.0 / 3.0), which specify 100mA / 500mA / 900mA.
Apple charger
Pre USB-C Apple chargers have a resistor between D+ and D- to indicate how much current the iPhone or iPad may draw. It's an unconventional approach as the communication usually works the other way round. They support up to 2A at 5V.
Qualcomm Quick Charge
Depending on the version of Quick Charge, the device and the charger can negotiate higher voltages. It always starts at 5V. If I'm not mistaken, you can draw 2A at 5V without negotiation.
USB Power Delivery
USB Power Delivery requires a compatible device, charger and cable. The device can ask for up to 20V at 5A (in 20mV and 50mA steps if PPS is implemented). The negotiation happens on the CC1/CC2 lines. USB PD will require a USB PD chip and a lot of software in device (about 50k of compiled code).
You most likely want to avoid USB PD as it's very complex. If you don't negotiate a voltage using USB PD, it will fall back to USB 2.0/3.0 behavior, i.e. you get 5V. But I'm unsure how much current you can draw. These chargers have power monitoring built-in and might cut your device off if it draws too much current (while older charger don't).
Summary
If 5V at 1A is sufficient, you shouldn't need to implement anything other than connecting GND and Vbus. If you need up to 2A at 5V, you might still get away without any additional logic for many chargers that offer QC or 2A ports. But it is likely problematic with USB PD chargers.
Implementing USB PD is a huge effort and most likely not worth it. As far as I can tell, there is no chip that implements it without the help of a MCU and a lot of code.
Overvoltage protection
I've implemented many USB solutions without overvoltage protection and never had any problems. I think it's only needed if your circuit is very sensitive. USB PD chargers have sophisticated power management and are unlikely to ever deliver higher voltages than negotiated. You should be more afraid of chargers implementing neither QC nor USB PD. They might deliver a short spike due to poor buck conversion regulation.