OK, here are some available options to you. First off you need to decided whether to all your members to add groups or not. See the options below.
We are going to use the example that you DO NOT want your members creating their own groups:
You would first need to go into Admin Panel> Settings> Membership Levels. Click the type of membership used for your members (ex. Standard). Scroll down to the "Add Group" option and remove the check mark, then save. This will disable your members from creating groups.
In the Admin Panel>Modules>Groups, you can create your preferred groups there. When creating the groups make sure that all the Upload options are set to Admins Only (default). This will block members from being able to upload anything.
Although this will work, this also denies the members from creating their own groups. Whenever you add a group, the "creator" has the option to say who can do what when it comes to uploading. So the only way to manage this is to take away the ability for members and then YOU become the creator of all groups with all control.
Another possibility is to disable the ability for users to add photos, videos, music, OR files throughout the whole site. Again, this can be done by editing the Membership Level described above.
Chris