I might have missed it, but all of the spark plugs should be removed for either test. In the case of a compression test it allows the engine to spin faster. And in the case of a leak down test it allows you to listen for leaks between cylinders.
The procedure for a leak down test is a bit long to describe (if all aspects are covered), but actually fairly easy to do. Might be easiest to search online for good tutorials in Italian? A small compressor should work fine. The test uses low pressure, just needs a constant supply of that pressure. So having some sort of "tank" (air reserve reservoir) on the compressor helps.
As to which test to do, it depends on what you want to find. If you are only looking to see if the engine is in relatively decent condition (not excessively worn or damaged internally), then a compression is fine and quick/easy to do. But if you suspect internal problems exist, and what to try and determine what those issues are, then a leak down test can offer more information. But a leak down test has a subjective component to part of it; if there is a leak and you want to determine the source of the leak, you need to do some detective work to listen for where the leak is and then make assessments as to why it might be leaking from there. So a little more understanding is required to benefit most from the test. Might depend on the experience and skills of the person doing the test. If you only use a leak down test to see if a leak exists, then it is no more beneficial than a compression test.