Going straight to the server:
There are some things that you can only do from a computer using a web browser such as Safari. Communicating directly with the server gives you more options. Here's how:
Launch Safari and go to gmail.com and log in with your Email address and password. Now you will see all your Email in the browser window. On the left hand side under the red Compose button, click on All Mail. Now look on the right side of the tool bar at the top and it will show you exactly how many Email messages you have archived. You could have thousands so don't be shocked. Click on the number and you can see the oldest first just to see how far back they go. If you no longer want them, check the boxes on the left then hit the trash can. You can do 50 at a time by clicking on the box at the top of the tool bar. Next, let's check some settings. Click on the gear on the right hand side of the window and drag to Settings. Scroll to the bottom of the page and you will see exactly what percentage of the 15GB of space you have use on Google's Server. Click on Manage underneath the number used, then on View details. This will tell you exactly what is taking that 15GB of storage. You may have Google Photos stored there and not even know it. By logging into the server and managing and deleting your mail from here, you can really clean it up. You can log onto any Email server the same way and check it's contents. It's a good thing to do once in a while just to see what's really there. Clean it up before you reach your limit and your mail comes to a screeching halt.