I can understand your concern that unfortunately WordPress by default have no option to add custom Avatar on your WordPress website. If you have Gravatar account on the same email from which you are signing up then WordPress automatically use your Gravatar profile Avatar.
Unlike for uploading custom Avatar from user interface, it is possible with WP User Avatar plugin. This plugin includes all the pro features, which you are required. Via this plugin even subscriber, editor, author and administrator can upload their profile picture easily from own interface and also can change/modify it in future.
Quite easy and fast way to add custom Avatars in WordPress. Hope that answered your question.