You MUST get rid of the grass before you procede. I suggest Round Up because it does not poison the soil or leave any residual chemicals.

Do not use any type of landscape cloth. In my experience it starves your plants (since you cannot add compost). Whats worse, it does not prevent weeds and grass from coming through, and really makes it difficult to remove the ones that come from down under.

Once you have a clean slate (see my first suggestion above), put in your plants, add a layer of compost, and then a layer of wood mulch. This should minimize new weeds until the plants fill in, and the mulch eventually breakdown into the soil. Good luck and happy planting!