Weed Barrier, Plastic Barrier
Arapahoe County Colorado
Good question, but I'm looking at the issue from the point of view of a horticulturalist, not an engineer. So if you need advice on whether or not the graded slope will prevent flooding, you'll need to seek someone else's advice.
A fair amount of research has been done on the pros and cons of plastic vs a weed fabrics. Plastic will prevent water from penetrating, but will also limits air from penetrating the soil. Plant roots need the air. So, if you are planning on planting anything on that slope, use a weed fabric. In fact, any existing plant nearby will probably be seeking soil and air in your newly graded area, so be aware of that.
As far as a rock goes, it gets much hotter than a organic mulches. Depending upon what is planted on the grade will determine what you will want to use.
Here is a document on mulches that you might find useful. https://extension.colostate.edu/topic-areas/yard-garden/mulches-for-home-grounds-7-214/
I hope this helps.