Better living through modern chemistry.
Before I would do anything with cardboard ect. I would go on into my local farm store and look for a weed killer that has only Glyphosate in it. This is what RoundUp is (RoundUp is simply an expensive brand name for a cheap chemical ). Skip the brand name stuff. This will go a long way in making sure Bindweed ect. does not rear its ugly face later. In about 10 days, most stuff will be good and dead. You will need a cheap hand pump sprayer to go with this.
You can then plant or, if you still want to, go ahead and smother. Make sure that if you use Glyphosate, there is good growth on the weeds/grass. It is a contact only herbicide- if there is very little leaf area, it will not be as effective. It does not have any residual ability nor does it remain in the soil.
