If that's the chappy:
https://support.hp.com/gb-en/document/c05563293
And its motherboard:
https://support.hp.com/gb-en/document/c05563293
Then you should have 4 x SATA ports, of which there should be two still available (DVD & current HDD occupy the other two).
However what you might not have is SATA cables in place (unlikely) - I had to procure mine for 870 model separately; not sure what's the story with 880.
Please also refer to this manual as I'm not sure if you have HDD caddies / trays in place:
http://h10032.www1.hp.com/ctg/Manual/c05535552
(from here: https://support.hp.com/gb-en/product/omen-by-hp-880-000-desktop-pc-series/15776604/model/17121455)
Best to check it beforehand especially as access is quite easy and user-friendly, it seems.
And yes, the disk you chose will be fine - depending on its intended purpose you may also consider buying faster SATA 2.5" SSD (more expensive per GB).