Disclaimer: this is not from experience so perhaps someone who do run servers with USB HDDs can comment on long term stability of USB as an interface.
Technically speaking, even USB 3 gen 1 (5Gb/s (gigabits per sec)) is far more than enough to saturate a broadband connection (probably under 1Gb/s). Assuming you’re going to use mechanical HDDs, best case they can transfer around 200MB/s (that’s megabytes per sec)), so no problem there either.
You might want to use external 3.5 inch HDDs as they have separate power supplies (less picky on power supplied from USB) and are much more likely to be CMR (which performs better than SMR, best if you check the specific model’s spec to make sure it is CMR) than 2.5 inch ones.
The cable one is just a regular SATA connector, since SAS HBAs can also control SATA drives (but not vice versa).
I believe the connector you are looking for is called SFF-8482. It is available in backplane and cable versions.
https://www.servethehome.com/sas-sata-cables-guide-sff8087-8088-8470-8482-8484-single-device-connectors/