it's funny how there are Europeans wishing to go the opposite way.. grass is always greener on the other side, isn't it?
What seems to work for most people is - apply for a EU university, hopefully in a field that's in high demand - start working part time in the very same field. When you finish your degree, hopefully the company that you worked for will be able to help you out with a work visa, if not, go for Masters degree to extend your stay. Once you've been there for 5-6 years, apply for citizenship.