The previous thoughts are accurate. I think that Oedipus is the character that merits our admiration. The fact that he endured a horrific set of circumstances is of vital importance. Oedipus endures a great deal and within this endurance lies the reason we should admire him. At the same time, Oedipus does not take his own life, but rather faces the truth that governs his state of being. In blinding himself as opposed to suicide, Oedipus becomes a model of how individuals must persevere through the difficult times in their lives in order to gain more insight and understanding into who they are and how they should live. I would say that Oedipus has his faults, but overall is worthy of the reader's admiration.
This is, of course, a subjective question. Some would say that no one should be admired, after all, this is a tragic play. It does not end well. As for Oedipus, it can be argued he is the least admirable, since his tragic flaw is hubris or pride. And he causes much harm to many people, even if it is unwitting. If I had to choose someone it would be Tiresias, the seer, in the play that has the ability to know, even though he is blind. Moreover, he is filled with courage to speak authoritative to a person as powerful as Oedipus. Also, he is the paragon of wisdom in this play. Finally, it seems that he is the one who fares the best in the play.
In Oedipus, we should admire Oedipus, of course. He is my favorite tragic hero because of his double blind ambition both to know the truth and to punish himself for not knowing the truth. Sure, he suffers from hubris and anger, but he expresses both only in pursuit of justice. In the end, he takes responsibility for his actions and achieves nobility in his suffering. He refuses to be a victim; instead, he becomes an emblem of suffering and knowledge, a truly religious being.
The great author and philosopher Albert Camus says that Oedipus achieves victory over his punishment, and I agree. Oedipus' life was a cruel joke fated by the gods. Instead of suiciding at the end, like Jocasta, Oedipus chooses to suffer and know the truth rather than escaping both. He is a hero because he hates death, loves life, and scorns the gods. A lesser man would not have blinded or exiled himself.
Like the Biblical Job, Oedipus accepts suffering as a necessary condition for mankind to better understand himself and the universe. Because of this, he becomes a blind prophet, like Tiresias.