Hey there, @KnightPlutonian!
I'd second @CountMike's suggestion about
reinstalling Windows from scratch. This would prevent the transferring of any redundant system files from your previous OS install. Also make sure you unplug the secondary HDD from the system if you decide to perform a clean install. This would prevent you from facing an OS confusion.
However, you mentioned that you would be reusing only the case and the HDD from your old PC. If you do that, keep in mind that changing the motherboard & CPU would require you to get a new Genuine Windows installation. The operating system is tied to the motherboard of the PC and changing it will require a new activation code/product key. You can check MS support for more details on that.
If it's the same motherboard and you simply want to clone the OS, then there are
a lot of cloning tools you can use. Just make sure you test if the SSD boots up properly before you format the HDD.
You can
re-partition and re-format the HDD from Disk Management in Windows by deleting the volumes & then creating a new one. Just make sure you backup all important data from the drive somewhere else beforehand. Reformatting it will erase all the contents on the drive.
Hope this helps. Keep us posted if you have more questions or concerns.
SuperSoph_WD