I think the final decision regarding a NAS vs an online service depends on how much space you need. I paid approx. $1200 for the NAS (Synology DS918+, $600), 16Tb of HDD and 2 SSD caches. Break-even vs equivalent storage is achieved in about 3 years. (my girlfriend is an avid digital photographer, and we have a lot of digital music.) If you don't need as much space, typically below 1Tb, I think you're better served with Dropbox or similar for about $100/yr/Tb.
I have a setup similar to what etn described above. A QNAP with 8 bays. Currently it's housing four 6TB NAS grade HDDs and one cache SSD. With RAID6 I have 12TB payload. RAID6 means any two HDD can fail at the same time without data loss. Also I can add another 6TB drive on the fly and have a full 6TB increase in storage.
In my computer I have a RAID5 of 3 cheap desktop HDD. Those are only the data vault, the system drives are extra. Originally setup in December 2012 with 3x2GB I had one fail a bit more than a year ago. Replaced it with a 3TB drive. The next one failed four weeks ago, I also replaced the next day with a 3TB drive. Once the last one is gone it will be 3x3TB and I can increase the storage size of the RAID5 array. I may pull that last one before it goes belly up on its own.
I regularly run a backup (rsync) from the internal raid with single redundancy to the NAS with double redundancy. The only problem now is the place burning down... For that I'm thinking buying a large archival HDD or two, which will take a (non redundant) backup to be stored in the office. Now if the house burned down and the drives in the office happened to be dead I'd know I gave it my best. All my negatives would be gone too. No redundancy there.
Anyway here is the important bit for our sceptical old school friends here: Yes, HDDs will fail and that is not a problem. But you need a redundant system. One drive fails eventually and you replace it quickly. The redundancy is restored. And because redundancy is no backup (only reliability) you backup to the other redundant system. The difference between digital and film/prints is that the latter can be quite stable in the right place. The digital system is more like a living thing requiring some ongoing maintenance/renewal. But the data on it stays the same. One day you'll replace the HDDs with whatever but the data stays save. Fileformats will not a problem either if you stay somewhat mainstream. All the old image formats from the 80s Amiga and Unix systems can still be worked with today.
The negatives from my childhood have been lost forever, btw. There are only some low quality colour prints left in albums. When I was an undergraduate student I didn't have my own camera, but ordered prints from those who took pictures on film. Those prints are what they are. Small and inflexible, hard to reproduce. It's amazing what pictures I still have from the early digicam days. They all survived being having been spread between a few computers and USB sticks. And can be reproduced at anytime to remind someone of those times.
I'm not saying digital storage is absolutely superior to film and prints. I think there is no clear winner: The digital system has some upfront cost and needs ongoing replacement and probably extension. In return you have digital data with no decay. So called bitrot is no issue for the informed photographer.
With film/prints it is possible to practice a store and forget system. But you may have slow decay if the stuff hasn't been processed well enough or the storage isn't good enough. Also it could take a lot of space, increasing like the digital data. For both ways you need to know what you are doing to be safe. Neither is impossible for the dedicated photographer.