Thanks very much for the replies/advice. I've read so many contradicting columns on the internet. Some suggesting to insulate the floor, and some saying this is a mistake, and others suggesting it is almost impossible to finish a basement floor without causing mold problems, which I don't believe.

So it sounds like maybe I should use some leveler, and put some 6mil poly on so it is pretty well sealed, and put a thin underlayment on top with 12mm laminate on that I should be good. Between the leveller and the laminate, that should keep anything that begins to curl down hopefully. Does putting the poly down increase my chances of mold? (I haven't seen any indications of mold, but the fact that the vinyl is popping suggests the basement has been humid at some points?)