Zotero gives each user 300MB of file storage for free. Citations take up little space. PDFs, snapshots, and other attachments take up quite a bit of space.
No matter which option you choose, Zotfile is a recommended Zotero plugin to manage your attachments: automatically rename, move, and attach PDFs (or other files) to Zotero items, and extract annotations from PDF files.
Caution: Moving Zotero to Dropbox, Google Drive, or other cloud storage will irreparably corrupt your Zotero library (though you can use these services to store attachments using Linked File Attachments).