Coyote Gun ??

Unless Remington has really gone downhill in the last decade someone gave you bad info. I also never thought much of the Savage but to each his own.  As for caliber, anything from a 222 to 270 is fine for yotes. Get a bolt action.
 If you intend to shoot a lot the 223 ammo is easy to find and would be less expensive than many others. Maybe a 223 with a 3-9 or 4-12 Nikon or Leopold. Don't know much about the night vision scopes.

Savage all the way
 
 
Big Green is a shadow of its former self...Remington is now part of the Freedom Arms, which is owned by a private equity firm; Cerberus Capital Management 
 
 
 
Confused yet? lol
 
 
 
 
 

http://dickssportinggoods.shoplocal.com/DSG/default.aspx?action=browsepagedetail&flashbrowse=y&storeid=2486131&rapid=1825914&pagenumber=1&listingid=-2056392360&ref=%2fdsg%2fdefault.aspx%3faction%3dbrowsepageflash%26storeid%3d2486131%26pagenumber%3d1%26rapid%3d1825914%26prvid%3dDSG-121104
Any opinions

I was never impressed with Savage but the new accu-trigger models are ok
I went crazy buying varmint rifles a few years ago and bought quite a few of them.
Any major brand should be ok starting out.
For scopes bigger is usually better 50mm or larger, my ATN was 75mm
Commercial loads should be good out to 300 yards and some of the premium loads will go way beyond that
22-250 might be better out past 500 yards but 223 should be good
If you buy a stock rifle getting a trigger job or dropping in a target trigger will make a big difference.
My Remington 223 and 22-250 both have rifle basics triggers set at around 5oz
AR 15 A4 elite and H&K PSG-! sniper rifle were set at around 8oz to prevent doubles
 

my model 788 22-250 is a tack driver.
Jus sayin!
 
BH

Not selling the Remingtons
You're too late to buy PSG-1 It was sold a few years ago for $6500 without scopes
You might of liked this one also

 
I bought this for shooting coyote and deer around the runways at Greater Pitt Airport but sold it after 911 because I was no longer allowed there.

you may have better luck finding a Stevens 200 

Are any of the mounted varmint light any good? Such as the primos 250?

http://www.dickssportinggoods.com/product/index.jsp?productId=1395303
 
With this scope..

If you want to use a 22-250, then go for it. It's a good gun. Buying a gun is like buying a car. You know what you want, then you start looking at other cars and you start comparing. I would use it too.