You need to keep those sprouts up and out of the water, so if you use something like a plastic dishpan, be sure to drill lots of holes in the bottom for drainage and rinse once or twice a day. You can also use buckets or storage totes. You can often get the shoebox size ones for a dollar on sale.
I sprout barley and oats from the feed store for my goats and poultry in the winter, but have had some difficulty getting it to the green stage without mold. I sprout it just a little to increase the nutrients and protein levels. I built a grow light stand last spring, and I plan to make renewed efforts to get to green grass with that this winter.
It doesn't really matter which grains you use to grow your sprouts, use whatever you can get. Just be sure to get food or feed grade grains, not seed grain, which is treated with fungicides.
Sometimes grains are harvested in damp weather and dried with heat and won't sprout well. Sometimes feed-grade oats are the screenings that are pretty worthless, even as feed, and there is not much in there to sprout. I have the most success with the barley I can get. You can also try wheat berries that you get at the health food store, or you could try the little packages from Bob's Red Mill. I can find those in the organic section of one of the grocery store chains here.