Pages are taking significantly longer to transfer from remote locations than from same LAN clients. Say 1s vs 100ms.
Data volume consumption is hard to predict, compression gain is very content dependent.
When installing IIS, during the selection of role services, check on Performance > Static Content Compression and Performance > Dynamic Content Compression too.
If you haven't done this during the installation, you can still add this via Server Manager > Roles > Add Service Features for the IIS feature.
After the installation of the features are done, all you have to verify is that the features are now active in the IIS Manager. Just check the configuration of the compression feature at either the server level or the website level.
If both compressions are enabled you can leave the rest on default or tweak as required. For example, you can turn off the threshold for the compression of static files.