It shouldn't really matter what port you plug the SATA data cable into as long as one of them isn't dedicated to RAID or something like that. (And I doubt that is the case.) Which port may slightly affect the order that the harddrives are detected and listed as though, worst case scenario you might need to swap the boot order in the BIOS for the harddrives if it tries to boot the old drive.
SATA drives are normally intended to be used with SATA power cables. It looks like the drive that is plugged in is using a Molex to SATA Power adapter, you might need another of those if the old drive can't use a Molex directly. (A Molex connector is what you are holding in the pic. Modern power supplies now usually have multiple SATA Power cables in addition to the regular Molex connectors.) If you can, you should double check any documentation you can get to verify if the old drive can use a Molex