It all depends on whether you plan to use the rifle for target practice or mainly for hunting. I have mine sighted in at 200 yards, knowing that it will be just a bit high at 100 yards, and a bit low at 300 yards. After 300 yards, .22-250 bullets tend to drop like a rock and require some good knowledge of the amount of bullet drop. Depends on your muzzle velocity, bullet weights, powder used, etc., but for coyotes and similar sized animals, I would sight in at 200 yards and place the cross hairs where you wish, without having to mess with thinking about vertical Kentucky windage and messing around with twiddling your scope knobs when the coyote appears.
I live at sea-level, and to compensate for altitude and local humidity, I like to wait until I get to where I want to shoot, then redial my rifle at 100, 200 and 300 yards. I make a mental note of the amount of bullet placement at each yardage. I find that the 200-yard range seems to give me the best all-around practical ranging for up to 300 yards.
Also, remember that the .22-250's barrel heat is a concern when shooting fast & furiously....especially when shooting on a hot day in a field full of prairie dogs or ground squirrels. I can get about 10 shots out of my rifle before the barrel gets too warm to shoot. Then again, it's a very expensive match barrel and I don't want to beat it to death. So, for shorter and faster shooting I use a .222 or .223 and my trusty Clark Special 10/22 rimfire. Their barrels do not heat up nearly as fast as the .22-250. The rimfire doesn't heat up at all...or at least an amount that I can detect.
Also, it's really a waste to use a .22-250 or .243, etc., for something like ground squirrels, unless you like those longer-range challenges.
You don't have time to do a lot of calculations when coyotes appear, then want to disappear a couple of seconds later. The .22-250 is a good caliber for those who don't use it every day, but keep in mind that longer shots of over 300 yards will require you to adjust your scope or put in some serious windage. But up to 300 yards....just sight it in for 200 yards and shoot the dog where the crosshairs are placed. Besides, your chances of popping a coyote diminishes greatly at longer distances unless you shoot from a rest with a heavier-caliber rifle. So, don't shoot with your .22-250 until they get within 300 yards.
Unless you are a crack shot and have had a lot of longer-range practice at really long ranges, the .22-250 places you at a disadvantage for super-long range shooting (say, up to 1,000 yards), in which case you should choose a rifle that allows you to use the heavier bullets. Which one to use? Hey....there are a ton of opinions and many rifles that are very effective at long ranges. If you reload, you can choose what you wish, but if you think you will find yourself out of ammo somewhere in the boonies, you may want to consider a non-wildcat caliber so that you can buy store-bought ammo after you have run out of your home-made stuff.