Since you assembled this computer yourself and your original drive is an EIDE drive, the PSU may not have come with the necessary SATA power connections, even though the motherboard "might" support SATA drives. I say "might" because without knowing what motherboard you have, we cannot verify if it supports SATA. And you cannot simply buy a cable and add SATA support to a motherboard. If there is no SATA controller and data connectors on the motherboard, you will have to buy a controller too, typically an add-in card. So make sure your motherboard supports SATA before you buy a SATA drive.
If you are certain your motherboard supports SATA, then for power, you will need to buy a power adapter as shown in your 2nd link in your post (#4) above. In your first link above, that is showing both the data cable (the red cable) which must connect to the motherboard, and the power cable (with the 4 wires). Since you are buying a "bare" drive, it will not come with a data cable, so you will need one of those too.