Start with a handcall. There are truckloads of e-callers sold to well intending hunters thinkin they need em. Many of them never call in a predator. Start cheap, add tools later to expand your repertoire.
Your .300wsm will definitely kill em deader than dead. But it seems that you think you'll get less fur damage with lighter varmint bullets than with heavier big game bullets. The farthest thing from the truth. You're gonna put a 2 holes in every coyote you shoot and probably wolf too. You can manage the size of the exit with heavier bullets slowed down a touch, holes will all be HUGE with the varmint bullets though. Try to work up some .308 velocity loads, maybe a touch less, using 150gr on up bullets.
Make sure you can see down wind. Most anyone can call in a coyote, most new hunters will never see them though. My favorite set up is callin cross wind with a shooting lane dead down wind to ambush the coyote as he circles.