Several things you can do to get more storage space. I have 15.8GB free with all updates installed. First, DELETE the Windows Update cache. When updates are installed, a cached copy of the downloaded update remains on the device, for no reason! If you've never deleted this cache, it will probably clear up 1GB or more. The files to delete are located in the following folder:
C:\Windows\SoftwareDistribution\Download
Next, by default, the Surface is configured with 1GB of virtual memory. If you navigate to Advanced System Settings, then the Advanced tab, press the Settings button under performance. In the window that opens, go to the advanced tab and press Change under virtual memory.
In the new Window, uncheck the auto configure box, and select custom size. Set the initial size to 256mb and the maximum size to 512mb and press set, then OK on the open windows and restart. You also have an option to not use a paging file entirely, which should be just fine as long as programs don't need more than 2GB of RAM, which they shouldn't.
You can also gain an additional 4GB of storage if you move your recovery partition from the surface internal storage to a USB flash drive:
How to backup the Surface’s recovery partition to a USB flash drive | Microsoft Surface Blog, Windows RT, Windows 8, Surface Pro, Xbox Surface, Microsoft