A cloud storage service is most suitable for backing up and accessing documents from multiple locations and devices securely. Cloud storage often includes features for file sharing, collaboration, redundancy, and strong security measures to keep data safe. In contrast, the other options, while having to do with cloud computing, do not match the client's specific need for document storage and accessibility: cloud gaming provides a platform for playing video games and does not store personal documents; cloud-based development environments are meant for coding and application development; a virtual private server, although it can be configured to store documents, would be overkill for a client specifically looking for document storage and is not the best choice when simplicity and reliability are priorities.