As someone who currently has 7.2 TB of my data on my private NextCloud setup (I would go with it over OwnCloud) – Let me chime in a bit.
– I would not throw this on a normal shared hosting account, a VPS or Dedicated Server would be best.
– Remote Storage has some quirks when NextCloud/OwnCloud that make some of the APIs/Sync Functions not work properly when syncing to remote storage.
– NextCloud/OwnCloud’s Index Tool can often get insanely slow when indexing remote storage (occ filescan –all) – I currently have a scan that has been running for 8 days
My recommendation is either to use SAN storage (if you have access to one) that you can mount locally on the server (and set NextCloud/OwnCloud’s data directory to. This way it appears as local storage. If you dont have a SAN, a dedicated server with a few 4 TB drives in a RAID would be the best secondary option.