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If you need near-line storage, consider using AWS S3, Backblaze's B2 or DigitalOcean's Spaces. All of these will require some kind of transaction time to do things with the files (we're talking milliseconds to a couple of seconds).

If you need on-line storage, such as for a database, then consider AWS with a big EBS volume or Digital Ocean's Volume Block Store.

All of these can be used with the smallest/cheapest VPS instance types... so you can pay $2/month for a micro-sized EC2 reserved instance and attach a lot of storage. A downside to this is that most providers top out at 16TB, which might be a scaling problem depending on what your business is. Even small image hosts are in the multi-petabyte range.