Self hosting principals aside, is this data actually important? If so, then don't fuck around with self hosting it. Are you looking for lowest cost? Then don't waste a bunch of money spinning your own disks.

Amazon glacier to guarantee availability and your own encryption to guarantee privacy.

It's currently running me about $4/month for around 10tb that I don't want to lose but just don't want to deal with. An equivalent HDD solution would be around $500, that's 10 years to break even assuming zero disk failures and zero personal maintenance time.

Plus it's guaranteed. Inherent multiple copies, has SLA, and there's no worry about the service just disappearing. It's they decide to shut down or raise prices or whatever, you can reevaluate and move.

Edit: Glacier and similar services are meant for archival which is the term OP used. You never expect to need it again, but can't get rid of it. Retrieval cost is mostly irrelevant, but yes much more expensive. (I'd wager still less expensive than a home RAID array.)

encode your data into the dna of an alien world so that it lasts for all time.

Depends how important the data is, how long is long term and how budget is budget, but assuming you don't want to risk losing anything, backup best practice is the 321 rule

3 copies 2 different media 1 off-site

I'd almost always say a cloud provider for your off-site backup, but if you don't want to do that, it depends how much you want to spend.

There's no guaranteed do-it-once-and-you're-done approach here, as all data can degrade. For instance if one of your backup media is hard disks, you're probably going to want it setup in at least RAID 5 and you want to be on top of swapping out disks when they fail. If you're thinking of the Blu-ray or tape approach, you're going to want to periodically check that the media hasn't degraded. You'll probably also want to plan to replace the backup media every half decade or so to be extra safe (e.g. BD-Rs have a lifespan of 5-10 years).

Honestly? If it's not that much data just throw an additional copy up on Google Drive.

If you have enough data: Tapes. Tapes are so hilariously cheap to keep. Write them and keep them in a fire proof box. No power needed to keep platters spinning. 45TB/tape!

CDs degrade over time and so aren’t the best way to archive data if you know you will need it again. If it’s just an ‘in case’ then it may be ok. Best bet is to buy a USB disk and then keep a second copy of it offsite. Also best practice to not use two of the same manufacturer drive.

Would probably help to know for how long, how much capacity do you need and what budget. Should also be stated external factors play a massive factor on how long a storage device can survive like enviroment, humidity and heat being the biggies

Edit in case I fall asleep: for the budget I usually would go with an external ssd just refresh the data every year or 2 it should be ok for 8ish years maybe even 10. For a write it and forget it method you'll want m-disc instead which are more expensive but if properly stored will last lifetimes so the failure point will be a usuable drive that can read it. If you decide to go the spinning mechanical drive route make sure to buy 2 (a backup for the backup) since they are a lot more fragile. Gold plated dvds/cds are also another write and forget option but have less capacity than m-discs

A couple different threat models to consider, hardware failure vs human failure. Things like RAID can effectively cover the hardware failure side and be fully transparent. Human failure is a bit more tricky. There are a number of old expressions about backups but one that's good to keep in mind is snapshots are not backups. They're convenient and easy to automate but if the system making them goes kerplooie they're pretty useless.

A tiered version is good for off device backup, using diff backups routinely to only copy the new or changed data with a periodic full backup.

Cold disks are great but make sure to test them periodically, nothing worse than looking to restore a chunk of data only to find the backup can't be read.

How much data? The answer will differ if it's a few megs of text vs a terabyte of videos.

Multiple methods, not really important which ones. I use an external hard drive plus I email zip files to myself.

https://en.wikipedia.org/wiki/M-DISC

I use multiple offline HDDs with a policy to keep n copies between them because it's by far the cheapest way to still own the data. It requires regular checks because HDDs are likely to fail after a decade or so and a bunch of HDDs are a pain to manage, so you will need tooling for this. I use git-annex for this purpose but it's not particularly user-friendly.

I use m discs. It's like a kind of high quality Blu-ray and should last thousands of years. I think your burner must support it though.

I don't know about your budget, but I'd do it onto HDDs. They're cheap and large. But use two and regularly check them like every other month or so. If one breaks, get a replacement. That's the most simple (if you have an external dock) and cheap solution that you OWN.

Also copy it at least twice onto each in case of corruption. Also use a copier that verifies (fastcopy, teracopy etc)