If your gonna buy hay or straw, both very well described above BTW, try to get it at the source. For horses and cows, try to get weed free. But for chickens, I use the weedy stuff. They will benefit from all the seeds that are in the weeds, and generally weedy hay has weed grasses as well. Weedy hay, is generally going to be less expensive. 1st cutting hay has more weeds then 2nd cutting, 2nd cutting has more than 3rd, etc. I like to buy it at the source as you can ask the farmer what he has, and tell him what you are looking for. Most all of us, can pinpoint the exact hay you are looking for in our 'stacks' as we know which and what part of the field they came from. I have read that chickens get crop bound from alfalfa, but I think that may be more of a free range vs. run chickens. chickens in a run may not have access to the pebbles and rocks needed to run the grinders inside them. Not sure, but there is hay readily available for mine, my mothers, my neighbors and most others in the area. Haven't heard of a problem identified to alfalfa around here.
You can generally see mold in small square bails as well. It will be a dark streak in the bail. pull out a bit, and you can smell the mold.
If the hay was rained on, then dried and bailed properly it will be dusty. I have never found an answer as to why, but my late neighbor figured wet hay caught more dust in the air when the rain made it wet, and it got 'stuck' on the leaves and stems. As far as causing respiratory ailments, I'm not so sure. There is dust and mold all over the place that chickens scratch and kick up all the time when eating or bathing. My personal opinion is one has nothing to do with the other and respiratory ailment is a symptom of a different underlying issue. Just my opinion, I have no periodicals, books, veterinary experience or medical council to back that up.
We use barley straw here, cause they grow barley for coors and budweiser. We only use straw for the nest boxes, shavings on the coop floor. Most of our straw goes into the garden to amend the soil. They do eat it, scratch through it and find the few seeds left over. Mine started nesting in the stack in the barn. Any local straw is used for bedding, my mother used to use straw for bedding then I told her about shavings. The shavings are easier to clean out with a shovel I think, so did she. But again, personal preference there. Straw bails do make a nice place to sit and enjoy your coffee in the morning while you watch your chickens and are also about half the weight of hay bails.