It will be fine if you have SATA. Make sure your old hard drive is a SATA drive. SATA uses a small thin red cable, IDE uses a wide ribbon like cable. If it is a fairly new computer it has SATA. And you can use your old cable.
WOW isn't an issue. You may have slightly faster load times with a newer drive.
This should help you, as it will give detailed instructions to help you along.
You will not have any problems playing games like World of Warcraft.
If you are adding a all you will need is the cable and a screw driver.