The "good" values depend more on what's before and after the regulator and doesn't so much affect accuracy. If what's coming in to the regulator is far away from the source, or the source has lots of ripple, a "bigger" capacitor at the input (10uF or so) can help with line transient response, i.e., keeping the output steady even if the input "bounces".
Conversely, putting a bigger capacitor on the output helps with load transient response, i.e., keeping the output steady even if the load (the thing that the regulator powers) instantly kicks up its current demands (fast switching load transient).
Basically, if your circuit works with 0.1uF caps on both input and output there's really no need to change it IMHO. Many regulators work fine with no caps at all (but check your regulator's datasheet....some have very specific requirements).
I generally start with 0.1uF on the input and output then add if necessary. Ceramic is a good choice.
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