I'm not a landscaper by any means, and they would be better to answer these questions, but I can answer from experience. I'm not sure how high you're going but always, always remove the grass. Landscaping barriers are only as good as the way you utilize them. I would want to completely remove any grass. You could use wood, but wood at ground level has a tendency to absorb water and crack, split and even worse, rot. To be sure your project lasts as long as you want it to, use bricks or stones to build up to the higher level.