Delivery size, not a master
Email signature reality
Outlook, Gmail, and Apple Mail all treat signature images differently. 300×300 at 72–96ppi is a common request so the photo does not explode to full width. If Mail.app still blows it up, the HTML width attribute is missing — fixing pixels here will not fix HTML.
Gravatar and comment thumbs
Gravatar serves multiple sizes from one upload, but some forums still ask for 300×300. Faces must be obvious at postage-stamp size. No fine text.
Do not upscale later
300×300 has very little detail. If you might need 1080×1080 for Instagram, keep the original and export 300×300 as a copy. This page is a shrinker.
File format
JPG for photos (small). PNG for logos. A 300×300 PNG logo is still tiny; a 300×300 photo JPG is usually under 50KB after a light compress.