Well, we've had recent reports of people successfully using the TIM voucher at the airport store, so I wouldn't worry so much about that. Personally, I'd be more worried about having to wait at a TIM store in line (if there is one) - and I just hate to wait, especially if I've just arrived from a long flight. I want to get going. I'd hate to have this TIM voucher in my hand and be stuck using it when I might get a Vodafone SIM instead or something.
Yes, I would highly recommend a SIM with data. The Skype idea was in addition to that, in case you can buy a SIM without international calling minutes (or not many minutes). To me, if you have to pay say 10 euros more for a SIM with international calling minutes in addition to data, it would make more sense to buy the cheaper SIM with data and buy the Skype credit - because you can keep it after your trip and use it in the future, if you don't use it on this trip. But your SIM minutes will be gone in a month whether you use them or not.