Buy a couple of external hard drives. They're cheap. Put one in a media rated fire safe.
Hell, I got a 128GB flash drive for $25 at Costco on Black Friday. Next year that should be a 256 for the same price.
But don't use flash for backups -- the long-term retention is poor. Magnetic media will last longer, assuming the entire drive doesn't fail. Which it will, of course. :)
You found a great choice for just music (it's cheap for Amazon to offer because so many people have the same stuff that they're not really storing all of the data multiple times).
For general backups, I like:
(a) Amazon offers an unlimited cloud storage deal that's pretty intriguing if you really use it - $60/year. Their terms make me a little twitchy, but I bet for most people it's fine.
(b) Also in the $60/year range is Backblaze, which is a quite nice option. I would opine that Backblaze is more likely to experience a catastrophic data center failure than Amazon is, but less likely to screw you over for some technical ToS violation, but that's a vague hunch, not a solid prediction.
(c) Dropbox and Google are both $10/month for 1TB, without the ToS twitch that AWS unlimited gives me or the "you only have one datacenter" twitch that Backblaze does.
(d) Crashplan's price is right; I'm out of date on that one.