All the green material will be very good for your compost. If you have enough material then you can create new garden beds by creating a kind of mix of thick mulch and compost (even on top of grass) to save you a lot of work. That's how i usually do it. You just make a nice long compost pile in autumn where your new garden bed will be. In spring you flatten it out and you are done. A big enough layer of compost will kill off most unwanted herbs. There is a lot of guides how to create new garden beds without tiling. Very good for your back. ;-)