I've not seen any mention of RAID HDD storage which can be a reasonably secure method of storage as well as others mentioned above. With the cost of hard drives being so low, you can affordably store a lot of data within a dual drive NAS. My preference is RAID 1 which makes a mirror copy of the drive. Performance suffers when writing to the drives, but when being used as archiving, this should not be a particular problem. It will still be much faster than writing to the cloud or to a DVD. Since RAID 1 mirrors the drives, if one fails or even if the NAS itself fails, at least one of the drives can be removed and inserted in another external drive or new NAS. For further protection, a 2nd NAS located off site and/or a cloud service like Google could add an automated insurance policy.
Currently, I actually do not use a RAID drive, but that doesn't mean I couldn't/shouldn't. I have a little Synology NAS, but I didn't set it up with RAID initially. When I can afford it (soon, I hope), I plan to get another RAID NAS and a couple of large multi-terabyte drives. In the meantime, I maintain my photos and data on my local computer with Google Drive set up to automatically copy specified folders to Google.
As far as privacy concerns when storing on a cloud, all I can say is do whatever floats your boat. Storing critical financial and, perhaps, medical data might not be a particular good idea with the exception of, perhaps, a service specifically designed for privacy or "secrecy".
Lastly, I'll readily admit I have not kept up with technology since I retired, so there may be even more reliable options out there. But, I am satisfied with where I'm headed with my archiving method.