Silencing the phone with the mute switch silences most sounds, including calls ringing.
Silence iPhone - Apple Support
The mute switch doesn’t turn off the haptics — the vibration — so the phone will still vibrate, and this vibration can be felt.
If you want your phone to ring, don’t silence it with the mute switch.
If you want finer control over what makes noises and what doesn’t, you can use what Apple calls a “focus”.
The “do not disturb” setting is one example of a “focus”m and you can enable and disable it, and can customize it.
You can set a focus to cause the phone to ring for any call, or to ring only for calls from specific people, for instance.
The User’s Guide that was linked earlier has more info, and Apple also offers (free) introductory classes for using iPhone at many Apple Stores. You can find the Apple class availability and scheduling here: Today at Apple - Apple
If you want a much simpler interface, Apple has Assistive Access available: Assistive Access User Guide - Apple Support