the ammo cost thing keeps coming up.
.17HMR is cheap, but takes a huge performance hit from .223 and is not
that much cheaper. .223 40 round bulk packs are around $24 while 50 HMR are up to nearly $20.
to be honest, i would just go out and buy a quality .22LR bolt gun before you buy anything else.
specifically bolt-action (or hinge) because it will handle
any ammo you feed it from acorns, .22 shorts, .22LR CBs, subsonics, all the way up to stingers/velocitors. some of these will not function or are not recommended in semis. you can, naturally, get a semi but you will be limited in your ammo choices and may have to cycle subsonic ammo manually.
ammo is diiiiiiiirrrrt cheap, pennies a round, and you can afford to go to the range or just plinking and shoot hundreds of rounds whenever you like. i have many guns but the most fun by far is a .22LR. if you do not have one in your arsenal then i highly recommend you get one before you blow your wad on anything else - you will not regret it.
as for coyotes? some people seem to think that you
need .223 and up to hunt them. personally i would not hesitate to shoot coyotes with CCI Velocitors if they were <100 yards.
this is one of my .22s - its a Russian TOZ-12, thats bedded into a Winchester model 52 Target stock that i refinished and stippled. it came with aperture sights which i can install if i tip off the scope. it cost me only $200, and i have a lot more expensive guns, but this is one of my favorite and most frequently used. CBs are the most fun ammo ever invented - out of 26" barrel like this they are extremely quiet - the loudest sounds are the firing pin on the gun and the bullet thwacking against the target. everyone needs at least one .22LR in their cabinet.