Which favicon files does a site need?
Today’s browsers need surprisingly few. A favicon.ico in the site root (here holding 16, 32 and 48 pixel images) covers every browser and tools that look for it by name. PNGs at 16 and 32 pixels give sharper tabs. The apple-touch-icon (180 × 180) is what iPhones and iPads show on the home screen, and the 192 and 512 pixel icons in site.webmanifest are what Android and installed web apps use. The download contains all of them plus the HTML to paste into your page’s head.
Designing for 16 pixels
A favicon is usually seen at 16 pixels, where detail disappears. A single bold letter, a simple mark or an emoji reads far better than a full logo with text. Check the browser-tab preview: if you cannot recognise it there, simplify. A strong background colour also helps it stand out against both light and dark browser themes.
The Apple touch icon is treated differently
iOS applies its own rounded corners and fills any transparency with black, so the Apple icon is always generated square and on your background colour, whatever shape you choose for the others.
Starting from a photo or a busy logo? Cut it out first with the background remover, and shrink other site images with the image compressor.

