cloud

The first and probably easiest solution would be to use a cloud service from one of the many providers available e.g., Google Drive, iCloud, OneDrive, Amazon Drive and so forth. There are different pricing schemes, sharing options etc. and I would suggest you compare the available options and choose one that fits best for you and your family. By using such a cloud service, you benefit from a relatively easy setup process and already incorporated remote sharing. The downside is that you lose control over your files once they are uploaded to the cloud, from a data protection and privacy sense. You never truly know how your data is being handled and might also get caught up within a breach of your cloud service provider.
Alternatively, you may also consider setting up a small home server or a NAS (Network-attached Storage). There are many options for customers to choose from, depending on their technological know-how and how much control they want, although at least some technological know-how is required to properly set one up. These enable you to have a home shared drive as well as public ones. This can again be achieved with the right know-how or services provided by the manufacturer. Overall, they are more costly initially and more difficult to set up, but enable you to take control of your data, how it is accessed, who can actually view and edit it, track data access and much more.