Because this is a play, the most obvious way that we learn about the characters is through their actions. Thus, when Agamemnon arrives home and is acting all tough and making a speech about how he honors the gods and everything, we might think he's a pretty cool dude. But when he lets himself be bullied by his wife Clytemnestra and walks on the purple fabrics against his better judgment, we can see that he's not all he's cracked up to be. As this example suggests, it's important to bear in mind that not all of the actions we see on stage reveal a person's true character; even though, at first, Clytemnestra acts like a loyal, loving wife to Agamemnon, it's only her actions at the end of the play – when she murders Agamemnon and Cassandra – that reveal her true character.
We also get a lot of direct characterization in Aeschylus's play, not from the narrator (there is none), but from the characters, who either talk about themselves or about other characters. For example, in the opening speech of the play, the Watchman characterizes himself as a long-suffering, diligent servant of his absent master, Agamemnon. At the same time, he characterizes Clytemnestra as a bad manager of the house, and says that Agamemnon was better. Because any character's opinion about himself or another character is inherently biased, any direct characterization in the play must be weighed against what we actually see of the various characters' actions. That's the only way we can understand what Aeschylus really wants us to think about the characters.
Agamemnon sacrificed his own daughter, Iphigenia, in order to get favorable winds to help the Greek fleet sail to Troy. This shows where his priorities lie. (Of course, you could also say that he is supporting his family here, because his mission is to bring back Helen, the wife of his brother Menelaus.) At the same time, Clytemnestra sends her and Agamemnon's son Orestes out of the city. We never exactly learn why. Was it to keep Orestes from worrying about his father's fate? Was it so that Orestes wouldn't find out that Clytemnestra was having an affair with Aegisthus? Or was it to keep him out of harm's way? If the last of these examples is true, that would suggest that Clytemnestra really loves Orestes, deep down. (She certainly loved her daughter Iphigenia, otherwise her motivation in the play wouldn't make much sense.) As you can see, family relationships in Aeschylus's Agamemnon don't always provide clear answers, but it is certainly an important aspect of its characters' lives.
What goes for Family Life in this play pretty much goes for Sex and Love as well. The fact that Clytemnestra is having an affair with Aegisthus heightens the sense that she is untrustworthy. But what was Agamemnon up to with Cassandra? The sex lives of the characters in Agamemnon are important tools of characterization, but they often raise more questions than they answer.