The difficulty with the historiography of medieval Italy is it is fragmented in case studies of specific cities. This variety makes for an incredibly rich historiography, but an intensely varied one. As far as general, introductory texts, I'm more familiar with English language historiography, but have read fairly widely in the Italian literature. Additionally, while the two are related, very often, northern and southern Italy are separated. This is both problematic and understandable.

Philip Jones's From Commune to Signoria is a bit old but amazingly dense and comprehensive account of Italy, focusing on the north. Highly recommended, if incredibly expensive.

Waley and Dean's The Italian City Republics is a fine textbook if you want a more accessible—and less expensive—option.

Wickham's newish book, Sleepwalking into a New World is quite good, short, and readable. He recognizes how the historiography is fractured and draws together several case studies to draw out general trends. The intro is a good introduction to the historiography of the region as well. Good place to start.

UPenn press has a nice reader of sources to introduce you to the types of sources you might encounter. It's got an unimaginative title, but it's amazing: Medieval Italy: Sources in Translation.

Eventually, if you're serious, you'll need to pick a city to focus on, but these books might help you select on. That said, Venice and Florence are fairly tapped out. Not to discourage you, but those cities have been really overresearched.