Welcome to growing, its a good size area to begin.
For soil improvement, you certainly can put the greenery down before covering, but it may slow initial growth this autumn (as it takes some nutrients to decompose) and may give home to slugs. Everyone does this slightly differently and there is no right or wrong, its more about being aware of what can happen.
In terms of how much mulch, it depends which weeds are growing, you need more and for longer if couch and bindweed are there. Horse manure will probably be quite full of bedding and is better composted for a year if so, for growing immediately I would buy some compost in sacks,
You can sow many salads, oriental leaves, kale at this time: check http://www.organicplants.co.uk for plants to buy which gives more options. I hope it goes well.