You have 4 SATA ports on your motherboard so I would think you still have one or two open. They are the orange ports at the lower right of your motherboard. You should be able to connect a SATA 1TB hard drive to any open port there.
SATA II and SATA III (sometimes referred to as SATA 3Gbs (SATA II) or SATA 6Gbs (SATA III)) are basically speed standards for SATA. Any SATA drive should work in there regardless of SATA II or III.
I say you should purchase the HDD and enjoy. Note that most HDD's do not come with SATA cables so I you do not have spares, you need one of those also - they're usually included with the motherboard.
Hope it helps