Suggested Italian books
 
While learning any language an important tool is reading; you should read anything you can get your hands on, make it fun, find reading material that reflects your hobbies and interests.
We are very lucky to have internet, it makes learning a snap
I studied French at school in Italy and when I came to the United States I did not know a word of English (well, maybe..Bye) but I had a lot of free time and started reading English books from the library and yes, at first I had to look up every single word in the pocket-size dictionary I had. 
But I have a good memory and massive determination and I learned and before long I could read just about anything in English. I could read anything long before I could speak.
By reading a foreign language you pick up not only vocabulary but grammar and syntax as well.
Once you start learning a new language you will realize that understanding something written will happen very fast, much faster than speaking it or understanding it when is spoken. Of course the more you read the faster the speaking and comprehending will happen.
Every language has its own idiomatic expressions, those are the tough ones, after 30 years in the States I still struggle with those. Another difficult thing is those words that are very similar in English and Italian, close enough that sometimes you don't know if they are English or Italian.
 
I started a new project for myself: reading all the books in the Strega Prize list.
The Strega Prize is the most prestigious literary award in Italy. It started in 1947 and it's been awarded every year since then, so, over 60 books so far. I am skipping on the list, some are easily found, others not.
Also, some I loved and others I can't imagine how in the world they won.
Check out that list at:   https://en.wikipedia.org/wiki/Strega_Prize , just in case the most advanced readers are interested.
For you beginners there are many choices, Kindle offers many Italian books and so Amazon. An Italian online bookstore I use often is: www.ibs.it  and  http://www.applauselearning.com/ has a large selection from beginners to advanced. I particularly like their Easy Readers collection.
I would not recommend newspapers, they are particularly difficult for beginners. Have you ever heard the term
"journalistic style"? well, it's taken to extremes in Italian.
And of course you can find "dual language books" although I don't think they are particularly useful for learning a language.
In any case, anything at all is good, whatever you like and however you want to do it...just, do it!
Happy reading!