Hi,
Windows 10 ver 1803 (Home and Pro) supports the following processors:
Intel:
Up through the following Intel 8th Generation Processors (Intel Core i3/i5/i7-8xxxK/U/G), 7th Generation Xeon E3-xxxx v6, and through current Intel Atom (J4xxx/J5xxx and N4xxx/N5xxx), Celeron and Pentium Processors
AMD
Up through the following AMD 7th Generation Processors (A-Series Ax-9xxx & E-Series Ex-9xxx & FX-9xxx), AMD Ryzen 3/5/7 2xxx, AMD Opteron and AMD EPYC 7xxxx Processors
Both versions support the latest processors from AMD, you don't need to worry about the cores, they will all be detected and supported.
As for 'legality' with Windows, you only need a legitimate Windows 10 installation on your PC or PC's to make them legal. It does not matter if they are only running Windows 10 Home. For a small business, you don't need Windows 10 Pro. It's not essential or indeed a 'legal' requirement.