Zotero is a "freemium" software, allowing 300 MB of free storage with upgrade purchase options. More info on Zotero storage plans here. Check how much storage you have used by logging in to your account at zotero.org.
The boxes below describe some changes you can apply to your Zotero settings to maximize your free storage.
The majority of Zotero storage space is used by PDF attachments, so one way to save space is to uncheck "auto attach in preferences.
Adding the OpenURL resolver allows you to access full-text articles through University Libraries' subscriptions. Zotero's default resolver is WorldCat.org. Go to Preferences-->Advanced to add Washington University in St. Louis as the default link resolver. The correct link is http://je5qh2yg7p.search.serialssolutions.com/ (visible in this screenshot). Click "Search for resolvers" to find and add it.