"Fix the Middle-East's economy".
I'm pretty sure that lack of money isn't a problem for most of the Middle East economies. Countries like Saudi Arabia, Qatar, and Kuwait are pretty well off. Of course not all of that money makes it down to the common populace, thanks to their dictator/royal governments. I can't think of an easy way to change their form of governments without massive upheaval, just like we're seeing in Iraq, Libya, and Syria.
"Build schools, staff them - an educated populace won't fall for the simple rhetoric of the mob-leader."
This will work, but will probably take well over 100 years. Again, you can't implement this with the type of social system and governments they currently have in place. Religion and tradition are so ingrained in their culture that the ideas of democracy and free speech are not only alien to them, but down-right heresy.
"Build infrastructure so they can actually communicate with the rest of the world"
Well ISIS is using Twitter, so they are communicating with the rest of the world, just not in the way we would like. All of the infrastructure, evidence, and knowledge in the world will do no good if you choose not to believe in it (hell, look at how much evidence we have for global warming and evolution that gets ignored in the U.S.).
The only solution I can see is to get away from middle-eastern oil as soon as possible. Their sources of funding will dry up, and the royal families/dictators currently in place will have no choice but to open up their society in order to build an economy that isn't based on oil.