Howdy Lex... just my 2 cents worth of the subject..
Quick turnover from woods to saw, the thicker the stock, the more notable the time savings.
Wood can be over cooked leaving it very HARD and sometimes difficult to work. ie chipping , tearout etc.....
Loss of color
Cost of kiln drying is carried over into the final price of the wood
Kiln drying can essentially bake in the hidden stress's found in wood. These stress's are revealed once the wood is cut..
Kiln drying is an effective way to kill off bugs/insects during the during the drying process
If you're dealing with a Mill, most likely you'll be looking at kiln dried wood
Pricing is all relative to local markets and availability of wood species.
Takes much longer than kiln drying. The thicker the stock, the longer the dry time.
Some folks suggest regularly rotating the stock during the drying process
Inventory turnover is a slow process, you need to have the room to stage the lumber during the drying process.
Wood is subject to insects and needs to be regularly monitored.
Depending on species, colors can be just stunning when air dried. IMHO this is the single biggest reason to go with air dried woods when the project calls for it. Although, not always practical or cost effective.
Air dried woods are less reactionary when cut. Internal stress's are slowly relieved during the curing process, making the wood less likely to 'relax' after having been cut. Perhaps saying less dramatic would be a better way of putting it.
Air dried woods are easier to work with hand tools and equipment. And can be argued less hard on tools and tooling.
For the hobbyist, finding air dried stashes of wood can be accomplished by being patient and diligent in your search. The pop up regularly on Craigs list here locally (SW Pa.) but seldom last very long. Usually smaller volumes with the occasional "big" find available. For a cabinet shop, perhaps no such a good idea to count on finding such stashes. I'd keep an eye out none the less for those "special" projects.
Walnut and cherry are the two most popular hardwoods in the US. Expect to pay a premium. Shop around and keep track of pricing. Get to know your local suppliers, both professional and hobbyist. I have found that the better I've gotten to know these folks, the easier it has become to work a "deal" on pricing.
Learn to use that saw you have!!!!!! A small time guy I deal with picked one up 2 years ago. There was a bit of a learning curve for him. Feed rates, changing blades etc...which blades and so on. Once he caught on to using the saw, there has been no looking back. AS mentioned earlier.. you can work out deals with the log suppliers. Wood in exchange for labor, volume discounts etc... lots of ways to make new friends
and become a very busy fellow.