Upload Files

As you've already noticed, Wysiwyg on its own does not include upload functionality. There are quite a lot of module supporting that and/or other types of media management already and integrating with them all from Wysiwyg would take up more time that we have.
Instead, we encourage each module to use Wysiwyg's API to present a small plugin to the editor which uses their own module for uploading or managing media. The Media module, and several others do this and are able to keep those plugins up to date with changes in their modules.

Some of the modules, like IMCE, do not include plugins for Wysiwyg/editor integration in their package. That doesn't stop you from being able to use IMCE with Wysiwyg though, since any other module can handle the editor integration on behalf of the module you want to use. In the case of IMCE, that would be the IMCE Wysiwyg bridge module. Once it has been enabled, it'll present a new "IMCE" plugin for the editors it supports. Enabling that button will in all supported browsers - AFAIK - add a "Browse" button to their normal image link insertion dialog.