Given the age of much local council legislation and the natural suspicion that electronic documents can disappear, I would think it advisable to keep hard copy of the critical documents, such as signed minutes, accounts and annual returns.
Otherwise, my view is that an electronic "cloud" service is a good way to provide storage and backup for documents. Last time I checked, the "Safe Harbor" provisions had been revoked for the USA, making Dropbox unusable by virtue of data protection considerations. An alternative is
https://www.sync.com/. You need a paid subscription to be able to have access to unlimited old versions of documents - an essential safeguard against malicious damage by staff or malware.
Also, bear in mind that principal authorities will often provide archival storage of documents free of charge.