[airstrike]

You get a single year of work authorization on an F-1. Only STEM graduates get an extra 2 years for a total of three. It's called OPT: https://en.wikipedia.org/wiki/Optional_Practical_Training

OPT is mostly only useful to give you extra tries on the H-1B, since the current system is a lottery. Since that lottery is once a year, OPT also makes it easier for employers to hire you at any given time so that you can wait for the next lottery. But no employer is hiring an OPT with an expectation that they will leave in 1 or 3 years, so the H-1B is still what everyone anchors on.

There's basically no way to get a green card straight after an OPT. There's also no way to extend an H-1B past it's 3+3 years.