After getting all of the requirements needed for the self-employed visa, you should schedule an appointment with your embassy (if you have not done so before going to Italy to obtain the documents).
FYI – your appointment may be be given to you months ahead.
Depending on how many days you have in your Schengen quota – 90 days within the last 180 days in total after calculating all of your visits to EU countries, decide if you want to wait for your appointment in Italy or at your own country.
You should make sure that you have some days left as a tourist after your appointments date in case for some reason you’ll be required to return to Italy to collect more documents. If your time as a tourist ran out in Schengen area, you may not be allowed back in until your quota limit resets itself.
Once you go to the embassy, bring all of the necessary items specified in the post about the requirements for the visa. Make sure you make yourself copies of everything.
Your embassy may or may not verify your income / bank balance records or your rental agreement. It depends on how many people ask for this visa in your country and how familiar they are with this process.
You would be required to tell them the date you would like your visa to start from (which should be when you are planning to go to Italy to start your relocation process), and to leave your passport there for a few days until your visa is ready.
And when pickup day has come, bring the receipt that they gave you and pickup your passport. Look inside that you have the visa.
Which at the moment gives you nothing in Italy other then the ability to work with a foreign tax account and to enter Italy.
You’re still not a resident. You can’t buy a car, You can’t rent a normal apartment, Open a resident’s bank account and get paid to it from your work, get your Italian tax account and so on or sign in to the public health system.
Having health insurance does not seem to be a requirement for getting the visa even though it’s obvious your will not be able to opt-in to the health system in the first few months. But you should get some travel insurance from your country until then just to make sure your covered. (about 6-8 months)
This visa gives you 1 year in Italy to finish your relocation procedures and become a resident. Which is more or less the amount of time you will need in order to stop being a tourist there and be able to do what a resident can do.
So if you think you’re finished – you’ve just begun! ?