First of all I would have to disagree with the majority here when they are saying a .223. I agree that it does limited pelt damage and is enough for a coyote but it is not the best coyote gun out there.
Having hunted many many coyotes (one of my obsessions all winter) I would say that you have an effective range of about 150 yards with a .223, the last year I shot coyotes with a .223 every coyote shot continued to run after shot. I did not have any get away that year (that were hit that is <img src=icon_smile_big.gif border=0 align=middle>) but all made me nervious enough to put a second shot in them..
If you are calling in coyotes to under 100 yards or if they will not know you are there then go ahead, if you are walking ditches and timbers and will be shooting at running coyotes that are fully aware that you are hunting them then go with a 22-250 or simular cart. they have much more knock down power and allow you to stretch effective range out to 300 yards without the big hold over or extended lead problems.
As for price of shells if you are only doing alittle hunting and not shooting a ton of shells you will not notice much difference. If you are buying on gun for all the things mentioned go with something that will allow you to reach out and put them down.
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