Even super slow HDDs are enough for Burst/Sia/Storj. For Storj your bottleneck will be CPU/RAM/bandwidth way before disk speed.
Besides, per gigabyte SSD prices are super high compared to disks which makes it a bad investment.
So best bet would be to get a cheap HDD with like 4-5TB. Any idea what the life span on those are while using Storj or mining Burst. Is it an intensive process?
I only mine Storj and disk activity is pretty low. But it depends on how much of the shared space is filled which takes months to get even ~20 GB.
I don't know about Burst, I haven't mind it in years.