Someone may disagree, but I have never seen a groundcover that will really choke out all the weeds. Groundcovers require maintenance. On a bank this steep, maintaining the groundcover may still represent a lot of work.

Have you looked at terracing the area? This can be expensive, but it will give you more planting area and easy control of the site.

Is a large rock cover with occasional roundup an option?

If you decide to use a plant goundcover, there are many many sites online that list a large number of possibilities. Google will turn up a list longer than you can review in a single night. Below is one such listing that has some of the more common options listed.

Here is a link that might be useful: VA CoOp Ext Selecting Landscape Plants: Ground Covers

My mom planted wandering jew in a similar area....no weeds.