My pick would be the .257 Wby; Roy Weatherby had it right, and it was his favorite hunting cartridge caliber. I've used the .257 Wby for most the small and big game in the North West including Elk and found it too worked just fine; with the right bullet selection for the game. My last {out of the eight or so rifles I've owned in that caliber} was an Accumark; it was target rifle accurate; come to think of it'…, I never did have a bad shooter in any of the Weatherby .257's I owned.
I believe in Weatherby rifle sales; the .257 Wby caliber ranks as number one, just edging out the .300 Wby.
As a Coyote and long range Deer rifle; well that's where it shines, I used a 100gr Barnes XLC BT and would back it up with Nosler 100gr Ballistic Tip BT which both shot into the same poi at 100 yards, and both were very accurate; with the speed going to the Barnes for long range, along with stronger bullet.
As to the comment by Marine Sniper on the 7mm. He's right about the better choice of bullets, and the application(s). I'm not sure I'd go with the 7mm Remington Mag today in your case. I'd look at something like the 7mm RSAUM; just think of it as a 7.08 Rem on steroids….. I think the RSAUM case is a great design and over looked by many today. I've used the case, also used on the .300 RSAUM for 1k matches at Raton NM and loved it; I shot with a friend that use the case on a wildcatted 6.5mm RSAUM and it was spectacular at 1k
A
Also the comment about brass always wholes true, yes 7mm Remington Mag will be a little easier to fined.
On a side note, I've seen the Marine Sniper do some very fine long range shooting with a 7mm, {not he 7mm Remington Mag} way pass where you thought it might end. Along with some very, very surgical 1k shooting and groups. Like me and my pick of the 257 Wby; there's a reason he pick's the 7mm. he's experience with the caliber.
Good luck with your project.
436