I am brutal and hardly green, so I spray weedkiller on areas and, when all is dead, and two weeks have gone by, I put my desired plants in. I choose one that even kills grass.
If I had a steep slope, I would use very coarse wood chips and dig through them to put plants in. You will notice the highway people put a green cloth type stuff down, or even spray with a fake green mulch. I would never hire a professional or go to such trouble, but I am, to put it politely, cheap.
Some tough plants are Junipers, Gro-lo Sumac, Cotoneasters and the perennial pea of the species latifolia. Beyond that there are a vast number of groundcovers. Do not plant creeping jenny, periwinkle or creeping Potentilla. They have designs on the entire planet.