I have a HOWA in .223 Rem. that works eceptionally well. Also, an H&R in .22 Hornet.

For varmints/coyotes/wolves, a .223 would be hard to beat. I've got a Browning with a 1:9" twist, and I have found that to be about ideal. I handload, and I can shoot 40 gr. V-max for bobcats, coons, and other small critters, 50 grainers for coyotes, along 55 gr. Sierra Gamekings and 60 gr. Nosler partitions for larger critters, such as hogs and deer.

For rabbits and squirrels, if you are planning on cleaning and eating them, the .223 is probably a little much. However, if you handload, you can load reduced loads using Blue Dot and make it shoot more like a .22 hornet or .22 mag. You might also use FMJ bullets on rabbits. If you get a good head shot in on them, it shouldn't damage the meat much.

I wouldn't use the .223 on squirrels, unless you are shooting them on the ground. The .223 bullets will travel a long way, even if you hit the squirrel. You'd be better off with a .22lr or shotgun for shooting up into trees.

From what you've described, I'd have to recomend a 25-06. Easily available ammo in a variety of bullets. Or you can roll your own . I say this because you included wolf in your list.
And it is still big enough for deer, bear, etc. You may want to check your local regs regarding legal calibers for all those animals. They may require a bigger caliber than .22 for the wolf.

i'd have to say .243. perfect for small animals such as coyote and bobcat and good for deer, as well.

I have a .243 Savage Model 11, I love it. Great gun all around. you can get fairly light bullets, for reloading yourself or in factory loads, but you can also get pretty heavy, atleast heavy enough for the game you describe. Might be large for rabbits and sqirrels, but it is a big range of animals you are tlaking about, it will be hard to get one gun to do it all. you would be better off buying 2. like a .17, or a .22LR, or a .204 ruger, and then a larger one, like a .243. Thats just my opinion, thats what I did.

Squirrels to Wolves in one gun????

From the list you gave, you'll need either more than onerifle, a smoothbore shotgun,or a combo. I wouldn't shoot any centerfire at a rabbit or squirrel, or shoot any rimfire at a wolf.

probably not wolves so would a 22lr. 50 gr. be good with a 3x9 scope?