I create a board in which there is a voltage regulator LM2596 (12V / 5V). At the inlet is an electrolytic capacitor (680 microfarad) and a ceramic capacitor (22 microfarad). Output electrolytic capacitor (330 uF). Should I install a ceramic capacitor on the out? If so, which capacity to choose?
Yes its a good idea to cut down on high frequency noise, as large a value as you can reasonable afford for
the purpose - 10uF or above starts to get expensive, and is typically SMT only, but usually large enough
package to solder by hand.
You would be wise to consult the DataSheet [link, below], as according to it, not just any capacitor will do. From the DataSheet [Section 9]:
Input Capacitor: "A low ESR aluminum or tantalum bypass capacitor is required between the input pin and ground pin. It must be placed near the regulator using short leads."
Output Capacitor: "Low impedance or low-ESR electrolytic or solid tantalum capacitors designed for switching regulator applications must be used."
Also, make sure to look through the "Typical Applications [Section 9.2]" as there are important considerations, such as proper connection configuration, etc.
For switchmode these days everyone uses MLCC ceramic if possible, have the lowest ESR and ESL, but
sometimes you need more capacitance, so electrolytic is put in parallel. Basically lower ESR/ESL
means lower ripple/noise on the output and less self-heating in the capacitor. That datasheet is
basically saying "don't use cheap electrolytics, the performance will be poorer than specified"
Linear regulators are another matter, the ESR constraints may be more critical to prevent oscillation.