I feel your pain! Grass is hard to remove once it gets established. However, it is better to get rid of it now rather than having it creep into your new garden. Our best results (other than a strong herbicide) have come from covering the area with heavy black plastic and letting it sit in the sun for a couple of weeks. Since the grass doesn't get air, sun, or water, it dies off and is much easier to remove. If you have a tiller (or can rent one) you can till the area several times. I would definitely try to get rid of as much current vegetation as possible---otherwise it will come back to haunt you :)

Another thing you can do, if you are willing to wait before planting, is do a lasagne-style garden. Lay thick sections of newspaper or cardboard over the grass, then cover with compost and/or composted manure. In the fall add a mulch of shredded leaves. By next spring the grass will have died and you can plant.

I've done it both the slow way and the fast way.

Slow ways-1.Cut a foot or so each year with a half-moon edger, remove and compost the turf, fill the newly dug hole with compost, plants then mulch. 2. Veilchen's cardboard method.

Quick but arduous way-take out all the turf and fill with compost, etc.

I expand my front flower garden each year with slow method #1. I take out the subsoil too, because it is awful fill. Seems like any way I do it I get weeds. But it is true-you have to kill or remove the grass. if you have a place to put that nice turf so it doesn't go to waste, it is good for filling in low spots in the yard.