A CHE is definitely your best bet. You'll need the che bulb itself, a socket to mount it in (they fit into standard bulb holders, but you'll need a ceramic one to be sure it's safe...there's a risk of melting with a plastic one), and depending on how extreme the temperature fluctuations are in the room your viv is in, you may need a thermostat. In most normal houses the temperature is reasonably constant, so a low power CHE should be ok and not overheat even without a thermostat. If you have a thermometer that records the max/min temps then you can check easily that it's not got too hot or cold overnight.
Heat mats aren't a great idea, even under the tank, as beardies can't sense heat from below properly and may end up overheating. Some people mount heat mats to the sides of the tank near the top so the dragon can't accidentally touch them, but that's a pretty inefficient way to heat, a CHE is a lot better and safer.