There are shared shuttle vans that aren’t standard taxis, which is what most people take between Atlantis and the cruise terminal. When we were there last (about three years ago) it was $4 per person. Those are lined up inside the cruise terminal fence ready to take people to Atlantis, and they also wait at Atlantis to take people back for the same $4/person. Tips are accepted; we paid $5/person with tip, largely because it was easy to hand the guy a $20 bill as we got out, for our family of four. Edit: Apparently it's now $5/person
There are also regular taxis, which have “taxi” written on the side, and a meter. Those seem to line up just outside the terminal fence, on the street. There’s a standard rate between Atlantis and the cruise terminal. Edit: there's a chart lower down this thread that gives correct prices for taxis between Atlantis and the cruise terminal. It's always going to be more than the shuttles.
I’d take a van again. The first van we took was a bit old and well used, and the driver stopped for gas on the way, but subsequent vans have been newer and perfectly fine. Taxis in Nassau also tend to be old and well used, so I doubt that would be much better.
One trip we pre-booked a private van to drive us around, and that was great. New van, working A/C, great driver. But I wouldn’t do that just to get to Atlantis.