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You might be surprised how cheap used SOHO NAS equipment is. I picked up a Qnap TS-869 a few years back for £300.
Like @Velocio I back up to external drives (shucked western digital 14tb white drives, £190 each on Amazon). I store my backups in a fire safe with another copy offsite. No cloud backup for me, it’s not economical.
FWIW I have different raid arrays for different use cases. My best drives (WD reds) store important data in Raid 10, but these sleep when not in use. For pseudo-cache activities like seeding, I use second hand WD greens (or whatever i can get my hands on) for around £30 a pop, in Raid 1 arrays or JBOD. If one or all the drives fail I don’t really care.
Edit. There’s a lot more to maintaining a stable, efficient Raid array than just a simple data striping tool. For example the single biggest killer of drives is operating temperature, so you do need good cooling, intelligent S.M.A.R.T monitoring, regular scheduled maintenance, etc. You won’t necessarily get that with a PC and a bunch of disks. NAS manufacturers have figured a lot of the problems out for you so the investment might be worthwhile in order to avoid a bad experience. Also SSDs are a very expensive (and often unnecessary) way to cache, they will fail a lot faster and only across a fast, cabled network are you likely to see a major benefit before they do. I’d try to save them for DAS use so that they’re only on when in use. I just pulled out a pair of 1TB SSDs from my NAS whilst I was experimenting whether I’d see any benefit.
My setup:
This is 32TB of disk with 24TB usable, and I've used 54% of the usable space... around 13TB.
I backup to a single external 12TB disk (which is now not enough, but I duplicate some of my files across SyncThing to other devices so I'm close to backup capacity but not yet at capacity).
Basically... I make my storage from lots of small, cheap drives with very high reliability according to the BackBlaze HDD survey ... this is their latest https://www.backblaze.com/blog/backblaze-hard-drive-stats-q3-2020/
I RAID for the purpose of not having to move and rebuild for the life of the disks I use... I've probably got couple of years in these ones.
I backup for the purpose of a fire or something dramatic taking out the house and disk storage... this is monthly as the data doesn't change at a really fast pace. I now store this off-site (at my partners place - upside they can use it to watch films directly from the HDD).
The most expensive components for me are always the NAS enclosure and the backup HDD (because a single large drive is always pricey and yet it makes performing the backup very easy).
I don't use Cloud backup for this stuff... the storage is cheap, but the network costs are not and the time to restore is painful (how fast is your internet connection?! add in how slow S3 Glacier is for read speed too!).
I don't over-invest in the RAID setup... it's not a miracle solution, if the RAID controller fails you've still lost everything. For me it's good enough to buy me time (a few weeks) from a single disk failure to have ensured the backup is up to date and to replace the bad drive. That's the only reason I have RAID6, so that I have time to be lazy after a first drive failure.
Now... for what you've described you can certainly purchase a 4-bay NAS and just do a RAID5 with 3 larger disks, add a 4th and expand the RAID later, and then also add in 1 single large disk for external backup.
But I guess the real question is: What's your budget?