Quick reference for some characters mentioned upthread.

Tyrion Lannister-The dwarfish youngest son of Tywin Lannister, the richest (and most vindictive) man in all the seven kingdoms. Tyrion is presently acting Hand (prime minister) to his nephew , King Joffrey. Tyrion is sarcastic and has a fetish for prostitutes. He's not overly fond of his family or their morals but they are his family. He is also one of the smartest men in the seven kingdoms and an excellent judge of human nature. He's not as vicious as the rest of his family but don't make him choose between you and them.

Arya Stark-The tomboyish youngest daughter of previous Hand Ned Stark. Before he was unjustly executed by Joffrey, Ned arranged for his daughter to be sent back home disguised as a boy. This plan fell apart when she was captured by enemies who don't know who she is. Arya is just a kid but has already seen a lot of killing. She's done some too. She saved the life of Jaqen H'garr.

Jaqen H'garr: He was a prisoner of whom other prisoners are scared. Because Arya saved his life and that of two other prisoners he told her that he would kill 3 people for her. He killed two but was shamed/forced into helping her when she gave him his own name as the final murder victim. There's a strong Rumpelstiltskin vibe to him as he has a very odd way of speaking, a warped sense of honor and in the last episode evidently killed at least a half dozen men virtually simultaneously and silently. So the viewer is not quite sure who or what he is but he's not your normal human warrior.

Varys: He is the spymaster of the realm and something of a frenemy to Tyrion Lannister. He manipulated Ned Stark into false confessions though he may not have intended Ned's execution. Very few people know what he's up to. He's survived and thrived under multiple kings. He is an eunuch and occasionally pretends to be quite effeminate in order to show people what he thinks they want to see. Notice in last episode he told King Joffrey he had no idea what was going on in the North but just afterwards gave Tyrion accurate information about what was happening a full continent away.

Cersei Lannister: Tyrion's big sister, wife to one king whom she had murdered, mother to another King and devotee of incest as her children are all fathered by her brother, Jaime. As Jaime is not around she's doing the do with her cousin. Something of a ur-feminist as she is quite frustrated by having to exert power through men instead of in her own name. Nowhere near as smart as she thinks she is but very dangerous in a "let's pull the wings off the fly because it's fun" sense. She set up Ned Stark. She also didn't want him executed but wasn't that upset by it. She doesn't like Tyrion at all for both personal reasons ( their mother died giving birth to Tyrion and Cersei blames him) and professional reasons (Cersei is upset that Tyrion gets to be The Hand).
Cersei thinks that all men can be manipulated sexually or by playing the victim and both respects and hates men who don't fall for that (her daddy, Tyrion, Ned Stark)