UF Accounts on Cloud Servers
If Zotero's paid data storage plans are not an option for you, you could use resources already available at UF and other tools online.
In terms of data storage, UF IT offers GatorCloud, a list of cloud servers approved for use with UF accounts, including Google Drive and Dropbox. So if you're saving PDFs, for example, you could consider saving and sharing your files across devices by using your UF account on one or more of those cloud servers.
You could also use the third-party ZotFile plugin to sync PDFs from your Zotero library to an Ipad, Android tablet, or mobile phone. Please see the ZotFile section of the Zotero guide from the University of California Berkeley Library for instructions on how to set it up and manage your files.