score:2
Coverage in Italy is good across all three main operators: TIM Vodafone and Wind. I would suggest Wind for it's value for money. With Wind you can get 100 minutes, 200 sms and 1GB for 10€ + 1€ (activation cost). They call this All Inclusive Ricaricabile. They also have an Internet-only offer giving you 3GB for 9€, which will however expire soon (8th February). See here for more details.
Vodafone recently swiched their pay-as-you-go plans to a senseless rolling contract scheme, forcing you to pay a minimum of 10€ to get a lousy 100MB of internet. TIM too switched to a similar system. Both this carriers however offer internet-only plans, here for Vodafone and here for TIM.
Upvote:0
The four main providers are: TIM, Vodafone, 3 and WIND.
Generally the provider is required to request your codice fiscale when opening a contract or giving you a prepaid SIM. Some vendors will refuse to give you a SIM if you do not have a codice fiscale, others will take a copy of your passport and simply 'calculate' your codice fiscale (alternative calculator here).
Once you have a SIM, it may take up to 48h for the SIM to be activated (this depends on system loads and vendor - TIM and Vodafone tend to be faster than 3 and WIND).
Regarding coverage you may want to see here and the links therein. Generally Vodafone and TIM have quite good coverage across most of Italy with 3 not far behind. WIND is comparable in the north, but falls back considerably when south of Rome and also is less reliable outside the cities.