Some people swear by optical media for archival and backup, but I've had trouble restoring data with different optical devices and media just 3-5 years after write, so I don't trust them.
Tape, on the other hand, is venerable and proven—so long as you stick to what the big boys use.
At the top end, DLT and LTO are both still very expensive, but as they age out, they end up on eBay relatively inexpensively. The mechanisms are very robust, repairs and replacements are readily available, media is in channels, compatibility is very good.
You can pick up a used-but-verified LTO-4 drive for $200 on eBay. SAS controller, $20-$40. Media ~$20/ea for 800GB/1600GB per cartridge. So you can get rolling at less than $300 for a complete backup and go from there.
If you want to run cheapskate, DLT-VS1 ("DLT-V4") drives often come up on eBay tested and working for $80-$100 for SATA, eliminating the need for a host adapter of any kind. The VS-160 tapes (160GB/320GB on a DLT-V4 drive) can pop up in boxes of 10 for $100-$120. So if you're patient, you can get rolling there for under $200 if you get lucky, though you'll wait around a long time and switch a lot of tapes to get your full backup done.
Just avoid helical scan tapes at all costs (AIT, DDS/DAT). The reliability is crap and the media quality is crap. Wine linear tape (DLT, LTO) is what you want if you're going to run data onto tape for backups. This opinion comes from two decades of experience.