You posted an image of 78xx datasheet even though you talk about 1117.
Input capacitor can have arbitrarily low ESR, although I suggest damping the input with a high-ESR capacitor as well, especially if the input comes from long wires.
On the output, a ceramic cap with series resistor does the trick indeed, but having two parts sucks IMHO. Also remember the minimum capacitance requirement of the 1117, and remember worst offender MLCC capacitors easily drop their capacitance by 80% under DC bias.
Tantalum is a typical choice on the output. Derate voltage by 50%., i.e, a 20V part is good to 10V. Do not use tantalum in the input because they are sensitive to unlimited surge currents.
Finally, I would seriously consider not using 1117. It's ancient, sold as LDO but by modern standards not very low-drop at all, have that stupid output capacitor requirement which increase the cost and area of the complete solution, even if 1117 itself is cheap.
Look at distributor parametric search and see which regulators you can get today; look for availability, good price, suitable footprint for you, then check the datasheet, modern parts often brag on the front page being stable with ceramic output cap, and such small values as just 1µF, with such low drop-outs like just 300-400mV. These modern parts are better in every regard and easier to use.