I'm interested in everything up to Napoleon, but if I had to pick I'm most interested in the Renaissance especially around 1570 to 1650 ish. Thanks in advance!
Haven't really read a lot on Venice, but I liked Venice, A Maritime Republic by Frederic C. Lane.
John Norwich has an excellent book called "The History of Venice".
If you're at all interested in the art/architecture side of things, I highly recommend Deborah Howard's The Architectural History of Venice and Patricia Fortini Brown's Art and Life in Renaissance Venice and Private lives in Renaissance Venice (the latter is more socio-culturally oriented, and super interesting if you want to learn about daily life).
For more general history, Thomas Madden's Venice: a new history and Joanne Ferraro's Venice: a history of the floating city are two of the most recent scholarly texts. I've flicked through the Madden one, and my Ren Art professor was pretty complimentary of Ferraro.
If you like opera, towards the end of your period, Opera in 17th Cent. Venice: the creation of a genre is a bit older now but very very excellent. Pretty easy read for an academic book actual, very smooth.
If you're still looking for suggestions I have plenty!
"Venice - A Thousand Years of Culture and Civilization" by Peter Lauritzen. He's arguably the best there is at Venetian history. The book was written in 1978 only about a decade after he officially started living there but he's still there today. It isn't a huge book - only about 220 pages but it gives you what you need to know. His love of art brought him to Venice which is part of why I've suggested it for you since you're interested in the Renaissance. Also, Peter was a lecturer (and tour guide of sorts) of mine when I lived in Venice so I may be a bit biased in my love and appreciation for him!
Someone else mentioned "Venice: A New History" by Thomas F. Madden which is also quite good. His style of writing is a bit dramatic for me so I personally wouldn't rush to re read it or anything. But that doesn't take away from it being very informative.
"City of Fortune - How Venice Ruled the Seas" by Roger Crowley. Also very informative. It reads like a story. I would reccommend this perhaps over the Thomas Madden book.
Anything by Deborah Howard as someone else has mentioned. I haven't read her books but have had her as a lecturer. Great passion for the subject!
And finally! For just a basic overview of Italian History I recommend "The Pursuit of Italy" - By David Gilmour
...I have more if you're interested. Haha!