Sawdust adds organic matter, helps lower the pH of alkaline soils, and repels some insects. Sawdust is so high in carbon that you'll need to add extra nitrogen, unless you compost it. Then spread 1-2 inches on the soil surface. You can turn it under at the end of the season. Newspaper sheets provide a barrier that weeds have a tough time breaking but water can easily pass through.
Newspaper breaks down over time, adding organic matter to the soil.
It's inexpensive and readily available. Deciding how thick to make the layer can be tricky. If it's too thin, it won't last as long as you want and weeds will pop up. Too thick, and you'll have to pull it up at the end of the season if you want to turn the soil or add fertilizer. How rainy the season is affects how long the paper lasts.