Europe Backpacking Route

I’m planning on backpacking for a month or a bit less in Europe, I need your help on finding the cheapest European route. A little background: I’m currently in California, flights from LAX to Barcelona seem to be $250 one way. Ultimately, I want to fly from a European country to Iraq to see my family. If I would to make the most out of my European trip, flying from LAX, where in Europe should I land and what countries should I visit in order before flying out to Iraq?