Gosh, there are all kind of options for a sunny slope. Personally, I lean toward flowering ground covers. You could plant soapwort, prairie winecups, or orange carpet hummingbird mint, to name a few. If you want taller, woodier ground covers, consider Pawnee Buttes sand cherry and Meidiland ground cover roses. Here's more info on ground on ground covers.

Sorry, I forgot to address your question about removing your grass and existing weeds. Yes, you should remove them. Although I'm not a fan of broadcast spraying (as opposed to spot spraying) herbicides, you might consider it to clear the area. Because you have both grass and weeds, you would need a non-selective herbicide (kills everything) such as Ortho Ground Clear. Just be sure to pick all of the flowers first and spray when the pollinators aren't out.

Another option is to suffocate the plants by covering the area with several layers of newspaper or cardboard.

How about "soil solarization" to kill the weeds, i.e. laying plastic sheeting over the area until the weeds are cooked?

I have only read about this method so it'd be great if someone with experience can comment.

Absolutely. Solarization would work.