Three main approaches, though two are variations on the same theme
You can't just stick an unlocked drive on there, it has to be the keys it has burned into the EEPROM. I think DVD drives might also be coded to it (recall reading something there when it was being compared to 360 mods where that was a thing)
However if you hardmod (any version but buying a mod chip which is easier said than done these days) or TSOP mod (easier to do with basic components but only works on 1.5 revision or older, the 1.6 family not having the option) it then you can put whatever drive you like in (pretty much any IDE/PATA drive here vs
https://xboxdrives.x-pec.com/?p=list for softmods). This is as they launch their payload early on where softmods take a second or two and come from the hard drive.
If you don't want to do that then you can do the hotswap method to install whatever you like on there (full custom dash + exploits to run it being what most would go for) and at that point you can boot back up to grab EEPROM and other keys and then go in for hard drive upgrade if you want to go that way. This however requires opening up the xbox and playing with cables vs just clicking a few times for softmods.
Do check it is not dust on the laser or something as well.