Ma Nature doesn't like bare ground. The sun burns and bakes the soil, the rains will wash it away. Ma Nature protects the soil. She tends to cover it in weeds. To avoid this cover the ground before Ma Nature can. Plant things close together so that when they are at their fullest they will shade and cover all of the ground. But most importantly - Mulch. Mulch suppresses weeds, and shades the soil keeping it cool and moist, It gives shelter for the organisms of the soil. It feeds worms and other creatures that are part of the soil food web. Eventually it will break down and become part of the soil. Healthy soil is alive. Nurture your soil. Feed your soil.
I tend to use "dirty" mulches under cleaner mulches. Anything that was once alive can be a mulch, but let's stick to plants. Anything compostable can be a good mulch. "Clean" mulches are those that you are comfortable having on the top layer and that won't attract flies, etc. Thus, clean.
Used Coffee grounds (UCG's) - where I work there are three breakrooms and I have a collection can by every coffee machine!
Newspaper, Cardboard, paper plates, paper towels, partially composted material, compost, and manure are all great under layers.
I like to use cardboard under paths and newspapers around my plants and then cover with ...
Grass clippings - my Dad once told me he was hauling bags of grass clippings to the dumpster, I gave him a look :( Now he drops them off at my house. My place of employment generates tons of free grass clippings as well.
Leaves - shredded leaves are best. They won't hold back water and break down quickly. If you don't have a shredder try mowing them with a lawnmower, then tarp them or bag them. They will store forever. Add water and keep them bagged for two years or more and you'll have leaf mold. I collect lotsa OPBL - Other People Bagged Leaves. More than 20 per year. I never have too many. People look at me funny when first I ask for them, but then they call on me every fall to take them away for them. Gladly! :)
I tend to layer grass and leaves as a top layer like a lasagna bed, but there are others...
Straw - works very well and there are no seeds!, but you have to buy it.
Hay - breaks down faster than straw, but usually has seeds. Usually slightly more expensive than straw.
Peat Moss - even more expensive that Hay! looks nice though.
Cocoa bean mulch - also expensive, but looks nice
Wood chips - the old classic for paths works in the garden too. It takes a long time to break down and can suck nitrogen from the soil if worked into the soil. Can be acquired free from tree trimming services or crews clearing power lines - best suited for perrnenials and around trees and on paths.
Pine needles - in large quantities can mess with the pH - they are acidic, but can be found for FREE and they look nice.
Play around with different combinations, layer them up like lasagna. Mulch before you plant and just pull back to plant things or mulch after you plant up to the stems of the plants. Just mulch.