Well, gonna have to research how Obama and Bush did it. If they can do it, Trump should be able to do the same thing.
>Which visa would a typical Mexican person apply for to immigrate to the US legally?
Well, how I came was, I had to apply for a Green Card to become a resident (legal immigrant) of the United States.
You can also apply for any work related visas that you qualify for (work visa is temporary residency only). Or, you can marry a U.S. citizen (permanent citizenship).
The good thing is, Trump plans to make the Immigration Process more efficient and faster for people who are legally migrating to the United States.