The only situations where trying to obtain Irish citizenship would be advantageous is if you wanted to live in the United Kingdom (Irish citizens have the right to live/work/retire in the UK) or if you have formal qualifications (bachelors/masters degree) in a STEM field. If you have formal qualifications in a tech field with educational degrees, you can often get hired in Ireland much easier than other EU countries due to the Irish Skills Waiver, and you would not need sponsorship.
You have to apply for and timely renew a residence permit. Documents which are required depend on the type of the permit. For work permits you need to demonstrate that you income is above the social minimum. The permit gives you the right to stay on the Italian soil and travel in the EU.
You need to rent a place to live and apply for the residency. Strictly speaking, residency is optional, but it will give you an Italian ID card, and will be required to receive a driver's license. IIRC you have six months before you need to get a local driver's license. Residency will also reduce utility bills and is required in some other situations.
After X years of non-interrupted residency (where X depends on your country of origin) you can apply for a citizenship. And it's a whole new story.
You also need to apply for an Italian fiscal code (and it will one of the first things to do).
Healthcare is guaranteed to all employed and self-employed, but you still have to have your ID, fiscal code, and a residence permit in order, and sign up for _Servizio Sanitario Nazionale_. The service to be renewed on each renewal of the residence permit.