You do not need to have any vaccinations to visit, and being part of the European Union means that travellers from the UK do not need specific medical insurance for travel to Italy, although you do need to fill in an E111 form for medical care. This should be done prior to travel (forms are available from post offices). However, you should still take out travel insurance when you go abroad in order to cover repatriation expenses in the event of sickness, and theft.
The hospitals in the city are of an excellent standard, and offer a full service for travellers.