I think you will find that chicken wire flexes too much and will hold too much trash due to the large holes.
I made a small one along the lines of Luremakers(without the framework) using two pieces of expanded metal, one 1" and the other 1/2". The pieces are rectangular and large enough to cover my wheelbarrow. I folded the edges down so they hook over the sides of the wheelbarrow so it stays in place. On the upper sheet, the folded edges help keep the debris from rolling off the sides. They are loosely joned/hinged at one end so they fold flat on top of one another for storage on the garage wall. I have two 2X4's with wood screws in the ends. I lay the sheets on top of the wheelbarrow with the joined end just barely overhanging the back edge(straight edge) I open up the expanded metal sheets(lift the upper sheet) and stand the 2X4's up at the open end. The wood screws go thru the holes in the metal and make the upper sheet stay at it's set angle, usually about 45 degrees(see attached drawing). I throw the shovelfulls of dirt I wish to filter onto the top edge of the upper sheet. As the material rolls down the angled sheet, the finer soil breaks up and falls thru into the wheelbarrow, while the roots, rocks sticks and grass roll/slide on down the expanded metal sheet and fall to the ground. You need to play with the angle a little. Too steep and some dirt will slide off with the debris. Too shallow and the debris won't roll/slide off the screen and will more easilly hang up in the screen holes. The flex in the expanded metal and the loose assembly means the upper screen bounces a little as each shovel full of dirt is tossed on the top. This movement helps keep the debris moving down the face and off onto the ground. I sort of developed a tequnique of plopping the shovel full of material down on the top edge and then allowing the tip of the shovel to drag down the angled face. The shovel tip rattles down the face as I pull it towards me and this also helps break up and separate the material. The second screen laying across the top of the wheelbarrow helps to catch any debris that happens to hit a hole just right and get thru the first screen. It works great for small jobs. I will ultimatly be building a larger version like Luremakers to use with my FEL bucket.