Your system came with a Seagate 1 TB HD. As you can see the drive within the system profile, are you sure the drive its self is bad? It could be something with the formatting or the OS install that's bad.
If you haven't already made a backup of you're data I would try doing that first. Using your system recovery disk to boot up your system you could try deleting the partition/s and re-install the OS and your apps.
If you want to upgrade your HD here is the IFIXIT guide to take out your current HD: iMac Intel 24" EMC 2267 Hard Drive Replacement.
As to what to use I would recommend going with one of the newer SSHD hybrid drives. You will need to make sure the drive you get is able to run at SATA II (3.0 Gb/s) check the specs sheet of the drive. You can't use the newer SATA III (6.0 Gb/s) drives unless it is able to auto set its SATA speed to SATA II. I would recommend going with a Seagate Desktop SSHD. There are others WD makes one as well but this is the only one I know of that runs at SATA II.