The fact that the bed has just been dug means that lots of weed seeds will have been brought to the surface, and these will germinate amongst any green manure or cover crop that you sow. Not a problem if you are willing to do a bit of hand weeding over autumn and winter. However, I prefer to sow green manure onto a fairly 'clean' surface (i.e. one with few weed seeds) so that it can be forgotten about until Spring.
Letting weeds germinate, then hoeing before you sow the green manure is a partial solution, but I'd be tempted to hoe once a week through autumn, so that all surface seeds germinate and are killed, then covering during the winter (simply to protect the soil from erosion and rain damage) with rough compost, straw, weed-free grass cuttings, cardboard, wood chip — whatever is available. In Spring you will just have to remove the mulch (to let the soil warm) and lightly rake over a couple of weeks later before sowing crops.
To recommend specific green manure crops is tricky as it depends on your soil, intended following crop etc, and is a large subject of its own. However, agricultural mustard and Phacelia are both easy ones to start with, and can be hoed off in Spring without much trouble.
