I used chicken wire; it was the least expensive option I found at the time. The drawback for me is that in winter, the snow collects on it, and I have to go in with a broom I sort of bounce it up & down so the snow falls through, or the load is too heavy. But, I typically only need to do that on very heavy snows, so it's only a few times a year. A 20x20 run wouldn't cost that much to cover in chicken wire.
Are you wanting to keep the chickens the run or keep them dry? To keep mine in I use a plastic netting from Lowes hardware, its pretty cheap and easy to work with. You have to thread some type of line between the 4 foot sections to keep it together but that worked great for me.
i use aviary or deer netting over my big girls pen area. Although, if i had it to do over (and i will at some point) i would use chicken wire. The netting can get torn and i do get squirrels crawling in between the overlaps, even though they are connected together every foot or so. i'm sure a determined predator of any type could get in through it. But my girls are locked up tight in their coop at night.
On my bantam pens, i only use hardware cloth, as they need more protecting.