Hi ace.
I did Giro de Toscana early May last year, it's a little cooler in the mornings than you'd think, so you might want to consider arm warmers/tights, or a long sleeve cycling jacket/fleece depending on your tolerance level. I target 1pair of shorts and shirt for every 2 days of cycling, and also a rain jacket, bike shoes, and helmet. Evenings are really casual, and that time of year possibly chilly, and bring comfy walking shoes (for those hill towns and uneven stones in the piazza!).

Not knowing how experienced a cyclist you are, I can share that I am not very, and since spring comes late where I am I target being able to do 40mi every day or so on a stationary bike (it's better than nothing!) for several weeks before the trip, and try to get on the road for as much as possible to re-learn how to shift and cycle in the real world. That area is rolling hills, so once you get the hang of them it's really quite fun!