United States – A way to stay in the United States for about 3 years after entering B1 B2?

Here is my situation:
My wife is a GreenCard (winner of the Electronic Diversity Visa lottery).
She got her GreenCard before our wedding.
I have a B1 B2 visa.
Currently, we are both outside the United States.

The idea is to move to the United States and begin a process of family reunification (which I understand would take about 3 years) and stay legally in the United States until the process is over. reunification is completed.

The questions are:

  1. What would be the cheapest (and most legal) way to stay in the United States throughout the reunification process (in addition to working visas; I think language course or university)?
  2. Is it a good idea to initiate reunification, while we are both in the United States? (maybe it would be better if I was outside, at the time)
  3. Any other advice, for the current situation?

Thanks in advance!