You want to look at a .223 if you want a long range number. Only because your not a handloader. .223 bulk or surplus ammo is as cheap as your going to get. Not a big deal if you just shoot coyotes, but if you ever settle down over a gopher shoot, you'll burn up alot of ammo. Plus the rifles are fairly mild mannered, and lower recoil/noise over say a 22-250. Yes, after a day shooting, you'll notice the recoil of the larger varmint cartridges. If you want more of a dual purpose rifle, I'd vote for a .243. Your budget will then allow you to look at the Mosberg atr, and the Stevens 200. But the #1 thing I will recommend to you...Buy a reloading setup. $150 is a damn good start with a good Lee kit. It'll pay for itself, and you'll really get to capitalize on any rifle you own. You can then pick any cartridge you want. Save up and buy a good scope too. One I really liked on my Model 70 Varmint was Bushnell's 6-18 Banner. It held up fine, the power was great at long range, and you could see well into legal light, and then some. Good luck with your choice.