If the mulch will not be thick enough to control "weed" growth (less than 3 or 4 inches) then a layer of newspaper can help. The granular pre emergent materials are pretty expensive adn do not add anything of value to your soil.

Kimmsr's suggestion will probably be the most successful because it is non-selective and will pretty well stop everything that is trying to grow that you have covered.

The product I think you are looking for is called Preen. You apply it to the soil and it kills many broadleaf and grass weeds when they germinate. It will not stop perennial weeds already established, such as quackgrass, and it does not harm some annual weeds, so they will grow right through it. It does not harm established perennial flowers/landscape plants you may have, but may kill any annuals you plant as seeds into treated soil unless they are of a plant family that is tolerant of the herbicide. You could use it with mulch as added insurance.