If economy is your thing, I doubt you can beat a 223 (if you use surplus ammo). Will ethically take Coyote out to 150+ yards easily if you're sighted in.
22-250 are great coyote guns as well, but are pricier for ammo if you don't reload. 22-250 will extend your range both for the coyote and at the range.
If you are considering rifle hunting for Deer in the future, you may want to consider a 243. Will drop coyote out to 400, and white tail out to 150+ with good shot placement. Will cost you more for ammo, but save you the price of a second gun later on.
If you think the "future" may also include moose, elk, bear, etc.. then get your 223 now, and start saving to get yourself a 270, 30-06, 308 or other "big game" rifle of your choice later.