The Starks are the first Great House of Westeros introduced in both the HBO show and the books. In the books they get most of the initial POV. This could have the effect of making the reader or viewer identify with the Starks. I certainly did and still do. Although the Starks are unelected nobles they appear, against all modern logic to be the "good" or "nice" nobles. Well as you know, things aren't always as they seem. Legends claim it was a Stark Night Watch commander who married a White Walker woman and then committed various atrocities before being defeated by the combined might of the Starks and Wildlings.
The Starks are rulers of The North, a region which is roughly half of all Westeros and is thus about as big as all the other realms combined. In culture and attitude the North is similar to real life medieval Scotland or Northumbria while in terms of size and weather it is like Canada or Russia. The North often has very long harsh winters. It's not densely populated or super wealthy. Much of The North's economy is based on frantically trying to produce just enough food to survive winter. Men and women are judged less on what they say and more on what they do. Northerners often have the prejudice that they're more plain spoken and virile than Southerners. Oaths are important throughout Westeros but are virtually sacrosanct in The North.
Although there is no class or gender equality, or democracy, The North in general and the Starks in particular appear to have less use for the complex Southern social hierarchies. Eddard Stark often sought advice from people of various classes. Eddard, and many of his ancestors, had a long history of treating people firmly but fairly. Good or bad, you always know where you stand with a Stark. House Stark and its vassals can't produce quite the number of soldiers that some other Houses can but they can rely on extreme personal loyalty in times of trouble thanks to past altruistic or honorable actions House Stark took. Starks can be very prickly about matters of honor and will often act in ways that confuse or infuriate others when honor is at stake.
Most Northerners, including the Starks, share little culturally/ethnically/religiously with the South and the Andal, Targaryen or Rhoynar descended people. They share much more with the First Men (Celtic analogues), many of whom's descendants are now derisively called "wildlings" and kept beyond the Wall. The North keeps to the old ways and The Old Gods. There are fewer Northern knights as knighthood is associated with the faith of The Seven. The Starks ruled as The Kings of Winter/Kings In the North for thousands of years before they bent the knee to the Targaryen invaders. The Starks probably have the oldest ruling line in all the Seven Kingdoms. Traditionally the Starks had few links to the South. Ned's father wanted to rectify that by having Ned's brother Brandon marry Catelyn Tully and Ned's sister Lyanna marry Robert Baratheon, Ned's best friend and ward-brother. As you know that didn't work out as planned when Brandon Stark stormed the Red Keep calling for Rhaegar Targaryen to come out and die.
The Starks boast descent from Bran The Builder, the legendary first King of Winter who 8000 years ago built Winterfell, Storm's End and The Wall, and established the Night Watch. He did all this after the Long Night, a period of night and winter that lasted a generation when the Others invaded the lands of the living.
Because The North in general and the Starks in particular tend to produce men inclined to direct action and not sly intrigue, Lord Eddard Stark was hopelessly out of his depth in the snakepit that was King's Landing and found himself outmaneuvered by rivals and falsely executed by the Lannister King. His firstborn son Robb Stark aka The Young Wolf is currently leading resistance to that King and has formally seceded from the Seven Kingdoms, crowning himself King in the North. He has also allied with his mother's people, the Tullys. Robb Stark is proving to be a surprisingly significant hindrance to Twyin Lannister, the head of House Lannister and the power behind the throne.
It is difficult to invade and virtually impossible to hold The North. The last person to do it (Aegon Targaryen) had dragons. Even then King Torrhen Stark considered trying to kill the dragons while they slept and continue the fight against the Targaryens before deciding he couldn't risk his people's destruction. The Stark sigil is a gray direwolf on a white field. Their enigmatic words are "Winter is Coming" . The words refer both to the Long Night and the constant struggle against the elements. As was shown when Robb Stark's wolf Grey Wind bit off the fingers of the GreatJon for questioning Robb's orders and right to lead, men of The North respect strength. No Stark will ever ask followers to do something he won't do himself.
House Lannister is the richest and most powerful House of Westeros. It controls the westernmost portion, unsurprisingly known as the Westerlands. This region has a tremendous amount of natural resources, primarily gold mines. House Lannister's investments and wealth have grown over the centuries. House Lannister rules from its capital of Casterly Rock. Lannisters are descended primarily from the Andal invaders. Their House founder was a trickster who conned the original owners out of Casterly Rock. The Lannister King Loren joined with the King of the Reach to oppose the Targaryen invasion. Fortuitously surviving the incineration of four thousand men, King Loren bent the knee to Aegon Targaryen and became one of his greatest servants.
It's neither widely known nor openly acknowledged but Joffrey Baratheon is really Joffrey Lannister. Cersei Lannister and Jaime Lannister committed incest, adultery and treason in cuckolding Robert Baratheon, a man whom Cersei Lannister loathed, in part because of physical abuse and philandering but mostly because he never loved her the way he loved Lyanna Stark.
Although Joffrey is King, the real power in House Lannister and thus in Westeros, is Tywin Lannister, Joffrey's grandfather, Hand, and the land's most ruthless, pragmatic and calculating warlord. Tywin has the total loyalty of some very vicious troops and is wealthy enough to buy many more monsters. It's unclear as to whether Tywin knows of the incest or knew of Cersei's plan to murder Robert Baratheon but it's a certainty that Tywin would permit no one else to judge his children.
Tywin's ruthlessness started decades ago. His father Tytos was a weak lord. Tytos Lannister lavished time on his lowborn mistress, giving her Tywin's late mother's dresses, jewels and finery. Lannister debtors didn't pay their bills. Lannister bannermen regularly disrespected Tytos. Finally, two Lannister vassals openly revolted. But it was the young Tywin who handled the revolt. He put down the revolt by the simple expedient of exterminating all the members of the rebellious Houses-men, women and children. Root and stem. Everyone. These acts made Tywin a dreaded man. After Tytos' death, Tywin had his father's mistress stripped and marched through the streets. House Lannister regained respect. Tywin intends that House Lannister's power continue after he dies. People laughed at his father. No one ever laughs at him. Tywin himself rarely smiles or laughs. Unlike his grandson Joffrey, Tywin seldom enjoys cruelty for its own sake but considers it a tool. Intentions don't matter to Tywin. Results count. He has low tolerance for flatterers or fools. And unlike the late Eddard Stark, Tywin Lannister has no concern for smallfolk.
Tywin had been former Hand to the Mad King Aerys but resigned after escalating tensions. Aerys was jealous that Tywin was getting more credit for successful administration than he was (and ripped out the tongue of a Lannister soldier unwise enough to publicly say that) while Tywin was deeply suspicious of Aerys' lustful designs on his wife, Joanna, and humiliated at Aerys' insulting rejection of Tywin's suggestion of a Targaryen-Lannister marriage involving Jaime or Cersei Lannister. During the rebellion the Lannisters stayed neutral until the very end, when they pretended to come to Aerys' aid but sacked the city, and murdered the king, his daughter-in-law (Elia Martell), and young grandchildren. Tywin had the Targaryen corpses wrapped in Lannister cloaks and presented to the new king Robert, as proof of his fidelity. His reward for this atrocity was to become Robert's father-in-law.