The batter receives credit for a base hit and an at bat. The baserunner is out, and the putout is credited as an unassisted putout by the fielder nearest the play. As for the rest of the rulings, the ball is dead, and all runners must return to the base they occupied at the time of the pitch, unless forced to advance due to the batter now reaching base. That is why the runner from third could not score on the play you describe, but since the bases were loaded, the runner on first had to go to second.
In OBR, these scoring rulings are found in 10.05(a)(5), and 10.09(c)(2).