That's a pretty tall order to fill. I'm not familiar with South Dakota regulations, but I'd verify first that a .223 is legal in SD for speedgoats. It is not legal in WY, the minimum caliber is .243.

That said, any centerfire is unnecessarily powerful for rabbits if you're hunting for the pot (cottontails). You may find the .17 HMR a bit stretched if you're shooting coyotes or prairie dogs at distances much over 100 yards. We've had a .17 along on a couple of trips calling coyotes and the results have been disappointing - a hit dog usually takes a .223 or .22-250 finisher.

For all but antelope, the .223's a great caliber. Ammunition's widely available, as are a number of decent rifles. If you search threads here, the Mini-14's reputation for accuracy isn't great. My personal favorite is the CZ527 Varmint Laminated in .223. Light enough to carry for coyotes, but just as much at home on a bipod over a prairie dog town.

Of course, if you need a goat gun, the .243's plenty adequate with 100 gr bullets and a winner with lighter bullets on varmints, too. If you're selling coyote pelts, be prepared to do sew some hides up.