Read Islamic history first, how it started, how Muhammad rose to power, what pre-Islamic Mecca and Medina were like, the major battles (Battles of Badr, Uhad, the Trench, Taif, Mecca, etc). Then you can read the Quran. Some verses refer to historical Islamic events, get something to supplement the verses so that you understand what Allah is talking about. The context of the verse, when it was revealed and why, is just as important as what the verse says.
You don't read the sunnah, exactly. The sunnah is basically how the Prophet acted in his life and how he taught his followers to act. For example, he entered the bathroom with his left foot first, so it is sunnah for Muslims to do the same. He kept a beard, so Muslim men keep a beard as sunnah in order to be more like Muhammad (now you know why so many Muslim men have beards). You will learn the Sunnah of the Prophet simply by reading the Hadith books and Islamic history.
For the hadith, there are 2 major collections: the Sahih Bukhari and Sahih Muslim. These are huge books consisting of various sayings of Muhammad, passed down from his followers down the years (definition of hadith). Not all hadith are authentic, but these books have the greatest number of authentic hadith compared to other collections, and they form the backbone of Sharia, Islamic culture, etc. Things like Muslim prayers and rituals come mostly from the hadith, and if you want to understand Muslim laws and regulations, you have to read the hadith, the Quran contains much less than you might expect.
I suggest reading an article on the hadith first, to understand what they are exactly, then read selected hadith from these 2 collections (it would be fairly time consuming to read *all* of them, but I do suggest you give it a try sometimes, but you need some understanding of Islam to properly understand it all). There are other collections, such as the Sunan of Abu Dawud, which are also quite authentic, but you don't necessarily need to read them. Sunnah.com contains entire hadith collections.
You don't necessarily read things in a linear order, just get a basic overview of Islamic history, traditions, etc and then read whatever you wish, if something confuses you, wikipedia is always there to help.