1. Hearts and flowers are an escellent choice. Once rooted you wont have to water to establish. It will spread by itself. Other ice plants would work the same.
2. Spanish shawl (Heterocentron elegans) is a little larger and takes a little more water. When established, it doesn't need water either.
3. Arachis pintoi is a good choice but it takes a little more trouble and water to start. Has a deep root and makes a good ground cover. Grows about 4 inches high.

Almost any tree would stabalize your slope.

let me know if you want more suggestion. You can google any of these plants to see what they look like and growing requirements.

Good Luck
Phil

How much of a slope is it? Our lot is very steep, but it has been terraced and that does wonders for planting things. Rock faced embankments with mondo grass growing in the crevices will eventually look like a grassy lawn and you won't have to mow it.