I use newspaper, usually two or three layers, covered with wheat straw. The newspaper really helps keep weeds and grasses from growing through the mulch, though they are pretty easy to pull if they do. The wheat straw serves two purposes. It keeps the newspaper from blowing away and it keeps the newspaper from drying out. If the newspaper dries out it may shed rain instead of allowing it to soak through until it gets wet.
I sometimes use cardboard boxes or brown wrapping paper between rows, covering that with wheat straw. I avoid newspaper or other stuff that has a lot of bright colors on it. Some doesn't bother me since the pigments they use for colors these days generally aren't nearly as bad as the ones they used to use, but I avoid sheets that are pretty solid colors. It's probably not necessary but I just feel better trying not go to extremes with that. I also avoid slick paper or cardboard. That can stop water from going through.
Like everything else, you'll find we use a whole lot of different things. We have different climates so different things work.
@flowerweaver can't use wood chips because of her climate. They would never decompose. We have different things available or often free.
In the past I used year old wood chips but pretty much stopped doing that. I'd put fresh wood chips on flowers or landscaping beds the first year over landscaping cloth, then remove them after a year to use for mulch in the garden. I have to remove them every year and replace them because they rot and form a real rich soil for weeds and grass to grow in. By using year old wood chips they have already partially decomposed so after another year in the garden they basically disappear. If I use fresh wood chips in the garden they are still around after that first season. You can turn them under and they will disappear eventually but they hurt my fingers when I'm digging around in the dirt.
Some things are pretty much self-mulching after they reach a certain size, like sweet potatoes, squash, regular potatoes, or cabbage, but I try to mulch about everything I can; tomatoes, pepper, eggplant, okra, beans, many herbs, melons, and some things I'm forgetting. It not only keeps the moisture in and the weeds and grass down during growing season, If it is left until the next spring it keeps weeds and grass from growing after harvest is over. It makes garden prep so much easier. I turn it under the next spring so it is my cover crop.