Try to estimate the amount of storage you are going to need for your images and compare that cost to a cheap NAS. I have a Netgear ReadyNAS 4 bay on my network and it does a pretty decent job of holding my files. The downside though is that drives can be expensive and they will eventually wear out. Plus, while having a NAS with RAID does provide you a level of redundancy to protect against file loss, it's not perfect and you can still lose everything. If you have a need for a high level of availability, reliability, and durability, cloud storage is the way to go. Just make sure that you shop around and find a provider that doesn't charge an arm and a leg.
I use Code42 for my local backup solution to protect my NAS. They charge $10 per month, per computer protected for UNLIMITED storage. They were a good fit for me because I had close to 10TB of files that I needed backed up so other consumption based pricing models quickly became too expensive. The downside though is that your upload/download speeds were shared with other customers and can be pretty slow.
Not sure it's the best, or that there is a best, but I use Cloudberry to backup to an s3 bucket. It hasn't let me down, I'm happy that Amazon doesn't know jack about what I store there (filename obfuscation + encryption) and as the above poster states s3 is plenty fast.What is the best software to use to encrypt locally having your own encryption keys?