Get better uploaded quality or save bandwidth: Change the JPEG compression-level of uploaded images and thumbnails.
The default image compression setting for JPEGs is 90%.
WordPress doesn't currently support PNG compression internally (none at all). There are other image-handling plugins that compress PNGs and GIFs, but they either require server-side tools or a 3rd-party service. For a Plugin using server-side tools, try 'EWWW Image Optimizer'. For a Plugin using a 3rd-party service, try 'WP Smush.it'.
First, install this plugin and choose your new compression level. Then install the Regenerate Thumbnails plugin, http://wordpress.org/plugins/regenerate-thumbnails/, and run it. All the regenerated thumbnails will be compressed at the compression % from this plugin.
Images uploaded while the plugin was active will stay at their original/old compression level (to recompress them, I recommend the Regenerate Thumbnails plugin). After you deactivate the custom compression setting will be removed and all new images will use WP's default 90% compression setting.