Adding a Favicon (Browser Icon) can help with SEO as well as make your site more professional.
They are best as a noticeable part of your logo, such as an icon or image (if you have one as part of your logo/brand) and show best as a square or 1:1 ratio.
Standard favicon sizes are 16x16px or 32x32px.
Standard apple touch icons are 180 x 180px.