For the first year you will be on a flexi roster, with no fixed pattern.
Commuting will be very hard, since EZY does not have direct flights from MXP to Rome.
Your options would be buying tickets with Alitalia or Air Italy, on which you would have no discount, or train, also expensive.
Much cheaper to look for a small apartment in MXP area or better a shared apartment. The area is not so expensive.
Even on a 5/4 roster, which you would get after one year, I doubt it would make financial sense to live in Rome. Commuting is doable in general, but only if you stick to the company network for the flights, but this is not your case.