While each historian gives a different perspective on events, for me, if you want to talk about 1066, you have to start far before it. The history of the Norman invasion was a series of many factors that had been building up for a long time. BTW, I was just writing off the top of my head and my post went a little longer than I anticipated. If you decide to take a TLDR approach, I won't blame you, but you can at least appreciate that there's more to it than the Battle of Hastings. And please don't pick apart my post for individual comments, it'll do all of us a huge disservice considering the length.
Let's look political real quick: Many people like to view 11th century England as being torn between "Europe" (aka France and, by extension, Rome) and "Scandinavia". In many ways, you can see a trend of "Normanization". The social position among many of the elites was changing. Many Normans were given land by the English King in order to ensure his ties to the south. This was very practical because many looked towards the East. Half of England was Danish at one point. In fact, our language wouldn't exist today if it weren't for a linguistic compromise that simplified it. Eventually, the King fled to Normandy, where he apparently promised the Kingdom to William (whom he could have seen as almost a brother for his support). I'm simplifying things a touch because it's a bit more complicated than that, but the history of Normandy, England, and Scandinavia is quite fascinating. You could just focus on someone like Emma and find lots of cool stuff to learn about.
On the continent, there was there was a debate about just what it was to be French. I realize this touches on warfare (it was a brutal time), but many petty Counts and Dukes were in a position of uncertainty when they realized they were stronger than their master, the King of France. In this politically uncertain time, the French King actually was forced to choose to support one vastly powerful vassal over another. He sided against William, which must have been a huge personal shock for him (I believe he had supported the King earlier). But the consequences are that it turned William from a French vassal (where any consequences he made would be under the rule of the French King) to someone who, after a promise for Kingship, believed himself an equal. The personal history of William is, in itself fascinating. He was a man whose father ruled Normandy, but was illegitimate and was always challenged for his Duchy. His father decided to go off to Jerusalem for a pilgrimage (which is a fascinating story in itself. These were men who killed for a living, but felt so guilty about it that they had to do great acts of penance to make up for it). He was always searching for legitimacy and was tenacious in his goals.
Then there's the socioeconomic situation in Normandy at the time, which had experienced a huge population boom because of agricultural success. Is it a coincidence that, for the last 60 years, Normans had been flooding into southern Italy and was defeating the last remnants of Byzantine rule in the area (along with defeating Muslims in Sicily and various Lombard Kingdoms that ruled). Is it a coincidence that they were among the most fervent fighters in the Reconquista in Spain? This is a period where Normandy stretched out and spread their influence across Europe (which is probably what the King of France was worried about earlier).
There's also Papal politics. William got a holy sanction for his actions in England. Some have argued that this was a proto-Crusade. At the very least, you see a Papacy that is strong in Europe (where 100 years earlier, it had been entirely discredited. They were either the person who could bribe the most corrupt Romans, or a direct appointment of the Holy Roman Emperor where the Bishop of Rome served the Empire as the Patriarch of Constantinople did in the east). Then there was a movement to strengthen the Papacy (too complicated to get into). Suffice it to say that, by 1066, the Pope was beginning to have the strength to influence the petty lords who served him in Christiandom. But it was a double edged sword. The next Pope was Gregory VII and he sought to directly challenge the belief of some that the Emperor was above the Pope. But he did so at the expense of all rulers in Europe. William's administration depended on his control over the church in England. There's an interesting Gregory-William battle that mirrors the Investiture Controversy with Germany.
I didn't even mention the government changes and the change of system that made England the best-run monarchy in western Europe. Or you could talk about advances in art and architecture (with art, there's a really interesting debate over the meaning of certain things in the Bayeux Tapestry, such as the use of Aesop's Fables that seem to actually be criticizing Willaim, with architecture, you could always just look at the prolific building of forts/castles in England after the conquest). I haven't even mentioned the working class (and barely mentioned the clergy). Unfortunately, my knowledge of peasant life in England in this period is limited, but I do know that William has left us with one of the most valuable sources to find out (the Domesday Book).
Of course, you mentioned only 1066 (and I assumed Norman Conquest of England as the vantage point). If you want to include the 11th Century as a whole, I recommend one of the best books I've ever read, The Making of the Middle Ages by R.W. Southern. He handles the period from a social, economic, political, and intellectual level far more than he does with warfare (although no discussion would be complete without it). Really an eye opening book for how everything we know today found its roots.
EDIT: For a biography of William, you probably couldn't find a better one than William the Conqueror by David C. Douglas.
