Large capacity exsternal hard drives are the best, preferably mechanical drives, not flash/thumb drives or Solid State hard drives. Solid state storage is very fast and impressive in use, but when it blows, there is no warning. The hard drive installed in your computer probably has a lot of free space but it is not removable and should not be used because it can't be isolated.
Using internal secondary hard drives to store vital backups is not to be advised either. While a secondary drive is under little pressure, it is still subject to conditions in the computer case which can change rapidly, an electrical short for instance.
What you have already..
Manufacturers don't supply disks anymore, but your computer should have a manufacturer recovery partitions are generally sized around 10 - 20gb. This is large enough to hold the basic Vista/Windows 7/Windows 8 image plus manufacturer stuff such that the computer doesn't flash up low space warnings, and small enough that they do not waste hard drive real estate. These partitions are good for re-installing the operating system and all that came with it when new, but only for as long as the hard drive is in good condition. This is a state that can't be guaranteed which is why manufacturers always suggest that a DVD recovery set is generated from the recovery partition.
What you should get..
Consider purchasing a 'one touch' external backup drive which comes supplied with backup software, or USB hard drive enclosure, a suitably large hard drive, and free backup software from Aomei. There is a link for this in the 'Software' section.
The software that I have seen supplied with 'one touch' devices is generally easy to use but does not allow for much choice, which may actually be better for the less technical user. Don't be fooled into believing that complex is better..
The cost of an external hard drive is peanuts when compared with photos of a child's life from birth, a once in a lifetime vacation to somewhere across the other side of the world, or any mega family occasion. It can save hours of re-downloading movies or music or YouTube videos. Convinced yet?