Constantia would be a better fallback than Times New Roman for Garamond, and Corbel would arguably be a better fallback than Arial for Proxima Nova. They may also have Gill Sans installed with some software, plus Open Sans is not bad.
I'd put something like:
"Adobe Garamond Pro",Constantia,"Times New Roman",Times,serif
"Proxima Nova","Open Sans","Gill Sans MT","Gill Sans",Corbel,Arial,sans-serif
BUT you MUST remember to test your websites with each of these fallback fonts, because fonts often differ greatly in metrics and in hinting (especially on Windows GDI Cleartype, as used in Chrome on Windows).