
Certified GKH Gardening Expert
Hay contains seeds, and will likely cause a different set of weed problems. It can still be done, as it makes a decent mulch if you can keep it from getting an infection. It just isn't the best for weed prevention, since it seems to cause as many problems as it solves.
When you use plastic to kill weeds, you do not leave it down as a barrier. This is TERRIBLE for the environment. It is mean to be taken up after it kills the weeds, then you you use the correct fabric weed barrier before laying your mulch.
Here are some articles that will help:
https://www.gardeningknowhow.com/garden-how-to/mulch/best-mulch-for-garden.htm
https://www.gardeningknowhow.com/garden-how-to/mulch/benefits-of-using-mulch.htm
https://www.gardeningknowhow.com/edible/vegetables/vgen/vegetable-weed-control.htm