if you are just looking for backup and occasional use, and dont need redundancy in case of HD failure, your best bet is Seagate 4tb portable hard drive.
it's basically the largest you can get for portable HD (single drive), for portable drives, even SSD's, you dont see the difference between TB and USB3.
also because it's small, portable, you can use a twelvesouth backpack to put it behind you imac, so that you'll simply forget that there is a external HD connected. and it will not break the simplicity of imac AT ALL. and since it only has one single laptop drive, it's extremely quiet. (something you definitely should take into consideration when buying a desktop HD, they are NOISY)
or, if you need redundancy, or want to try fancy thunderbolt, WD has a similiar portable 4tb thunderbolt drive. everything else remines the same, just it utilizes thunderbolt so it saves you one USB port. and it contains two 2tb HD's, that you can use RAID1 to save you from hard drive failure, or use RAID0 for faster speed.