Iirc, Rubios plan would grant most things you mentioned but not give citizenship to illegals.
The first place to start is to not give anchor babies citizenship. Will five less incentive to anyone to come to the US.
Here is a New York Times story related to the plan by Marco Rubio. According to this story, his plan is similar to the one the president has proposed.
Rubio Outlines Elements of His New Immigration Plan
This is the first paragraph of that NYT story:
"Senator Marco Rubio of Florida, a Republican who is on a talking tour to publicize his proposals for an immigration overhaul, said on Thursday that tighter enforcement at the borders and in workplaces would be central to his plan, which would also offer legal status to millions of illegal immigrants."
Now, all that said, I've not read his actual plan, but from this story and what I heard on FOX the other day does seem to indicate a path to citizenship.