Asparagus are good. We got an allotment last year (and a second plot this September).
Not a fan of rotavating myself. It just chops up the weeds and puts them a few inches down.
My wife removes EVERY single weed by hand.
Personally,I remove the nasty ones by hand (ie big roots or couch grass) than then turn the soil over with a spade. This puts the smaller weeds 8 inches underground and makes most of them die. The remaining ones can be picked out in the spring.
Garlic is also a great crop, as are shallots.
Courgettes are great, but need space.