Which type of 100nF capacitor is best for 78xx regulator output?
There is little point to ever use a tantalum when a ceramic is available for the same cost.

Actually, I'd use a 1&micro;F ceramic on the output and a 10&micro;F ceramic on the input.  The 7805 will be plenty stable with those, and that will help with transcient response.

The reason you see 100nF (let's not use ".1&micro;F" baby talk) a lot is for historical reasons.  Back in neolithic times when a caveman first carved a 7805 from a chunk of silicon, that was about the limit of cheap and available ceramic caps.