Well, since there are lots of steps, large and small, that led to the Trojan War, this is asking for a judgment call, and I'm going to leave that up to your judgment. If it is hard to track what happens in the different books of the Iliad as you read it, you might add the enotes guide to the poem to your reading process: http://www.enotes.com/iliad/
That way you'll have a guide.
As far as the beauty pageant, that's a great story. All the gods and goddesses were attending the wedding of Peleus and Thetis. All of them, that is, except Eris, the goddess of discord. She always starts fights, so she wasn't invited. To get revenge, she threw a golden apple into the gathering. On it was written the words "For the fairest." All the goddesses wanted it, and that became the beauty contest. Zeus for once was no fool, and dodged the judging, giving it to Paris. Paris chose Aphrodite over Athena (who offered knowledge and success in battle as bribes) and Hera (who offered wealth and political power). Aphrodite "gave" Paris the most beautiful woman in the world: Helen. However, she was already married to a Trojan, so Paris had to steal her. That started the Trojan war.