How to backup a large (100gb+) microsoft sql database for occasional "offline" use?
If the primary goal is to save money (i.e. not licensing Standard, let alone Enterprise, edition) you’ll need to be creative and accept a certain amount of inconvenience. Some ideas:


Purge any data you know you don't need
Break it up into smaller database that do fit on Express (by date, by table, by subject, whatever fits)
Export it to an open source system (Postrgres, MySQL)
Save it in on the cloud (Azure, others), using a plan that best supports infrequent access
Store it outside of a database, on a per-table basis (ASCII file, Spreadsheet)