If you really want to immigrate permanently to the U.S you should do the masters and go to a regional.
The contacts you make will be just as important as the education and experience .
It will be difficult to keep the green card if you spend a few years at Turkish. The experience you gain in Turkey won't be as valuable to a US airline as you think.
I have a green card and now live in the U.S . I thought I would have no problem getting on with a US airline with all of my foreign experience and bachelor's degree. I couldn't find anything decent so I commute to China from the US .