What's your budget for this endeavor? Both initial outlay, and ongoing annual costs.
Also, what does the data budget look like? Is it mainly an initial capture of size X, then updates of size Y? If so, what are X, Y, and the update interval?
Some things you ask about, like data integrity, could be at least partly addressed by distributing identical copies across multiple storage forms. For example, multiple NAS devices, and multiple online storage services. You'd need checksums, like the above noted SHA ones, but you wouldn't directly need an error-correcting scheme, because errors would be handled by the redundant storage.
You also haven't mentuoned security. If you need to encrypt the data, then you'll also need to store the keys securely. If this is long-term, then that means secure against natural disasters or your own death. And now that Death has entered the scene, it brings legal issues into play (who owns what, who is responsible for what, etc.)
