I am a physics/math major, and also a new US immigrant. I think I know intermediate level Java, intermediate data structures and algorithm design, and, some machine learning (with Octave), HTML, JavaScript, and Linux command line. Problem is I neither have job experience nor concrete project examples.
My question from the professional programmers out there is, considering where I stand, which of the following strategies is more likely to improve my odds of getting a programming job:
Learning new skills toward a particular niche such as web development, mobile apps, etc., instead of doing random projects?
Finding non-paid internships in a particular niche, instead of working on my own or open source projects?
Creating self-directed projects, and publishing codes in Github etc.?
I understand that these are not mutually exclusive. But my question is about the quickest strategy. Also, please don't hesitate to suggest me your own experience and/or what you think is a better strategy. Thanks in advance.