Turning leftover shelving into a small rolling cart

I have leftover shelving boards and four small casters from another project. I'd like to turn them into a narrow rolling cart for cleaning supplies, preferably with two shelves and a handle. The main concern is wobble; it will be taller than it is wide. Would a plywood back panel or diagonal brace make the biggest difference? I want something functional from scraps, not a piece of furniture that falls over when pushed across a tile joint.