Welcome to the community, Aron!
Just like @Barty mentioned, you shouldn't have any issues with the SATA II (3 Gb/s) HDD on a SATA III (6 Gb/s) port on the motherboard. Mechanical hard drives are not able to exceed the bandwidth provided by a SATA II (3 Gb/s) port, so a SATA III (6 Gb/s) would be even less likely to affect its performance.
Solid-state drives (SSDs), on the other hand, definitely NEED a SATA III port, because a SATA II one would definitely limit the transfer rate performance of the drive.
Here's a similar thread from the community that you might find interesting -
SATA II vs SATA III HDD,
Hope this was helpful. Best of luck!
SuperSoph_WD