I'm glad you've got rid of the stones and the membrane. It's a good start.
It's likely that the soil beneath will contain lots of weed seeds that have yet to germinate. With some water and light many will germinate and grow by next Spring. Putting manure on top doesn't make a lot of difference to that. If used to cover the surface, manure may act as a mulch and temporarily supress the growth of some weeds.
As figrat has just said, the roots of green manure can help to break up the soil.
Personally I'd leave it open, and add manure (either brown or green), and let the air, rain, frost, and worms get to work. You'll have plenty of weeding to do in Spring whatever you do.