There are four main types of bedding (shavings, sawdust, straw, and wood pellets) traditionally used in horse barns and I will discuss the pros and cons of each. There are other types of bedding (peat moss, shredded newspaper, corn husks) but as I have never used these or seen them used, I can't really comment.
SHAVINGS. This type if bedding is, hands down, my favorite. It is very absorbent, it looks nice, it smells nice, it is easy to clean with a muck rake, and you don't have to bed it at deeply as other types of bedding to get the desired effect. Most shavings are made from pine and while 99% of horses don't have a problem with this, I have known at least two horses who were allergic to pine and thus to the bedding as well. It is also the most expensive of all the beddings and can sometimes be difficult to buy in bulk. If you can find a way to get shavings blown into your barn (and have a large area to keep them) that really is your best option. It will be less expensive overall and you won't be dealing with endless brown bags to dispose of. A barn I used to ride at as a child did this and it was great. It also saved on time for those cleaning the stalls. All they had to do was pile some shavings into a wheelbarrow and dump it in the stall. 
SAWDUST. This would have to be my second favorite bedding. It is very similar to shavings with three big exceptions: it is much less expensive (and you can get it at a variety of places including directly from lumbermills at wholesale cost), it must be bedded twice as deeply as shavings to prevent elbow rubs because the texture is much more fine, and it can be a problem bedding for heavy horses due to the (you guessed it) dust. Still, this is a really economical option for large scale barns looking to cut down on their bedding costs and still keep the horses happy. Because sawdust rarely comes in bags, you will need a place to have it blown into (a shed or empty garage works; I have seen some barns use a corner of their indoor for the bedding but I am personally not a fan of this) but it is much less expensive than bagged shavings. My college used sawdust at their equestrian center to great results. They did have a few heavy horses, but avoided excess dust by lightly watering the top of the sawdust down once the stall was cleaned. 
STRAW. As I said before, the barn I manage uses straw. It is not my first choice, but I've learned to live with it and even appreciate it on cold winter nights when I can pile it high in the stalls and the horses snuggle down into it. Straw is pretty expensive - often as much as hay - and can be difficult to store as it is usually sold by the bale and will take up as much room as your hay supply. Horses have also been known to eat straw (talking to you, Cami and Poppy) though I haven't seen one colic or have health problems because of it. Straw also isn't that absorbant and we have run into problems (especially in the summer) with urine building up in the stalls. I can clean a stall bedded in straw faster than a stall bedded in shavings, though this was an acquired art after a few months of experimenting with different types of rakes (FYI, pitchforks work the best). Straw also needs to be bedded pretty deeply to get the desired effect, which is not very cost effective. We have eighteen stalls right now that get bedded down with straw. On average, we go through ten bales of straw a day (less in the summer). That averages out to be around 3,650 bales of straw a year - yikes! 
WOOD PELLETS. Ten years ago this bedding was almost unheard of and now it is used almost as much as shavings. Personally, I am not a huge fan of wood pellets. I think they can work really well for a small scale barn, but we tried to use them for a month at the college equestrian center and it was an absolute disaster. When I tried to use them once for Darwin he ate all of the pellets and had a big belly ache the next morning. Theoretically you only have to use one bag of pellets a week once you have the stall initially bedded down, but I have never found this to be the case. I don't like how the pellets are very hard for a day or two before they start to bed down and I also don't like how you leave the wet bedding in to absorb. But hey, I know some barns absolutely love wood pellets and would never use anything else... so to each their own. 