What are the three choices that Odysseus makes in Books 13-19 of Homer's Odyssey? How else could they have been made?

Odysseus makes a few important choices in these books. Let us look at a few of them.

Book 13 marks his return to Ithaca. Here, he encounters Athena in the disguise of a shepherd's boy. Together, they devise a plan for his return to his court. He decides to disguise himself in order to test his wife, Penelope, as well as his subjects. He could, of course, have returned and declared himself without any disguise. 

In Book 16, Odysseus (whose identity is by now known only to the swineherd Eumaeus) cannot stop himself from rebuking his son, Telemachus (who doesn't not recognize his father) when Telemachus expresses doubts about his mother's fidelity. In so doing, he nearly makes his identity known to Telemachus. He could have restrained himself. Eventually, because of Athena's intervention, he decides to make his true identity known to Telemachus.

Books 17-20 form the climax of the epic. In Book 18 he decides to return to court in the disguise of a hapless old beggar. He begs from Penelope's suitors, thereby exposing their characters. Again, he could have decided otherwise. He has good reasons, however, for making himself known only gradually. He then decides to challenge the real beggar, and chooses only to break his jaw instead of killing him.

In Book 19, he decides to remind Penelope of shared memories while at the same time keeping up his disguise. He need not have tested her in this way, but he seems to deem it necessary.