Wood shavings -- universally available at a reasonable price, absorbent, somewhat resistant to packing/matting, light and easy to handle, slow to break down, may be dusty. Beware Cedar because Eastern Red Cedar contains aromatic oils that are highly irritating to the lungs and birds have delicate respiratory systems.
Straw (the stalks left over after harvesting grain) -- comes in bales or chopped and in different textures depending on which grain it was. Traditional animal bedding over millennia, absorbent, often inexpensive, composts readily, can be prone to packing/matting and thus may need to be fluffed up more often, may grow mold if it gets wet, hollow stems *might* (or might not), harbor parasites IF they are present (this is debatable). An intact bale with one string cut is an EXCELLENT boredom buster for a flock that has to be confined for some reason. Intact bales make excellent chicken-level windbreaks.
Sawdust -- fine and dusty. Fairly absorbent. Scoopable. May be available for free but be careful of the source to not get treated wood or Eastern Red Cedar. Easy to handle, composts faster than shavings but not as fast as straw.
Pelleted Horse Bedding -- Easy to handle, highly absorbent, may be expensive. Composts like sawdust because that's mostly what it is.
Wood Chips -- Coarse wood chips from a tree trimming service are generally considered the gold standard for controlling mud and odor in the run. Do not pack or mat. Highly absorbent. May be available free from a municipal waste site in variable quantities, may be available free by the dump truck load from a tree trimming service. Bagged mulch is similar but be sure to get it free of dyes and fertilizer and the coarse kind rather than the finer variety.
Hemp Bedding -- Trendy among the eco-conscious. Expensive. Scoopable. I have no direct experience with it.
Pine Straw (the long, soft needles from the Loblolly and/or Longleaf pines) -- Locally available in the US southeast. Inexpensive or free-for-the-raking. Not particularly absorbent. Highly resistant to packing/matting. Dries out on top quickly after even the heaviest rains. Very slow to break down.
Shredded Paper -- light, absorbent, may be free for the labor of doing the shredding. There's a long thread about it here:
Using Shredded Paper for Coop Litter - As Good As Wood Chips?
Fall Leaves, Lawn Clippings, and other yard waste -- highly variable in availability and composition. May be excellent, may need extra management to keep it from packing and matting. Free. Uses material you would otherwise have to dispose of.
Ground Corn Cobs, Rice Hulls, etc. -- Locally available materials worth looking into if the price is right.