I would go with the 22-250 in either the remington 700 VSSF II or a browning m-1000 eclipse. Preferably the eclipse, since it is the most accuate rifle I've ever shot in any caliber. I would top it with a leupold vx-III 4.5x14 40mm scope or a 4.5x14 44mm zeiss conquest.
The 17 is not as good for bigger small game such as coyotes, IMO.
I like the jump in velocity the 22-250 has over the 223 so I can still push the bigger 60gr bullets down the range at 3600+ fps. The 223 factory ammo will barely push a 40gr bullet at 3600. Velocity means alot in a .22 caliber.
I figure that whatever a 223 can do, a 22-250 can do just a little better. You can buy the milsurp ammo cheap for a 223 but its only good for shooting really. I would'nt even classify a 17 in the same category. The 22-250 ammo is cheap enough. Youre looking at a 400yd rifle easy with a little practice. The 223 and 22-250 should cost the same in whichever rifle you buy.
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A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed. 2nd ammendment, U.S. constitution
While I have a 17HMR and love it, you really can't compare it to a centerfire, they are just in a different league when it comes to performance on game.
The .223 can be cheap to shoot and very accurate, really depends on what kind of ammo you buy or if you handload. Also the guns really are not any more expensive than any other, unless you are considering getting a tricked out AR. Other wise the standard bolt actions shouldn't cost anymore than any other caliber, might even be cheaper.
The 22-250 has much better velocity and range. However the ammo can be more expensive if you are buying premium ammo. I have also heard of premature barrel wear on this caliber.
I will add another one to your line up. A nice .243 would fit nicely. Depending on what weight bullets you used you could use it for varmints, medium game and even deer. Pretty versatile round. And easy to find just about anywhere.
Paul
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I didn't climb to the top of the food chain to eat carrots! (Ron White)
Barrel life these days is not a thing in .22 cals. Newer powders and modern tech have fixed all that, hence the 220 swift comeback. Taking care of a 22-250, the barrel should go at least 2500+ rds. I wouldnt worry about barrel life in any 22 anymore.
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A well regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed. 2nd ammendment, U.S. constitution
.17, .223, OR 22-250
