Before you get into nitty-gritty like passes, start by getting a copy of Rick Steves Italy (for this purpose, it needn't be the very most recent edition). Read it. Also, watch his videos on Italy here: https://www.ricksteves.com/watch-read-listen/video/tv-show. Then, look at as many other guidebooks as you can get your hands on (friends, library, etc).
Doing these steps will help you make sure that Venice, Florence, and Rome are indeed where you want to go. Be careful of well meaning people who will try to add things to your trip - "You can't go to Italy and miss the Amalfi Coast! You must see the Cinque Terre! Get out of the cities and see rural Tuscany! Don't miss the great food in Parma and Bologna!" While these are all fine destinations, you only have 10 days. Italy has several months of "must sees on a first trip" and you have to be careful not to include more than you can enjoy in your short time (I only get 10 days on most of my trips, so I know how hard it is to cut things). So, if you include one of these other places, you have to cut something else.
Next, decide how many days you want in each place. As Ken so accurately said, everyone will do this slightly differently, including those who say you should only go to two and spend more time in them vs. those who say go to all three for a taste. They are quite different, and you really can't go "wrong."
Assuming you're seeing all three, definitely book flights into Venice and out of Rome, as this direction is much easier for airport-to-city transit than the reverse.
Once you know exactly where you're going, and how long you're spending there, only then do you need to worry about things like passes and advance tickets. You will want to get these things, as well as advance train tickets, to reduce costs and avoid missing out on some things - but for June 2016, it's too early to get them, so don't worry. You will definitely want to buy the 2016 edition of Rick's Italy book, and it has all the details about booking advance tickets for attractions (you may need help with the trains, but the people on this Forum will gladly help you with that).
Happy planning!