Aluminum electrolytic or ceramic capacitors for linear regulator input and output?
It doesn't usually matter, but be aware that some linear regulators--the popular LM2940 series, for example--may be unstable if the output capacitor's ESR is too high or too low. As the datasheet for your regulator doesn't seem to say anything about that at a glance, it should be fine with any capacitors you pick, but see the edit below for a warning.

Non-polarized capacitors more than about a microfarad used to be rare and expensive, which is probably why the datasheet shows polarized capacitors being used. Today, you can get 10μF ceramic capacitors for less than $0.30 each.



Edit: As @ThePhoton points out, this regulator may be so old that multi-microfarad ceramic capacitors, with their inherent low ESR, may have been a far-off pipe dream to the engineers writing the datasheet. So this may still be unstable with too low an ESR on its output, so unless you want to test its stability under different operating conditions with the ceramic caps, it may be best to stick to aluminum electrolytics. After all, that's probably what the IC's designers had in mind.