First off, I really don't know much about predator hunting yet. I recently retired and have some opportunities to go after some yotes, and have decided I want to see what its all about. Never had much against coyotes, but one tried to eat my miniature schnauzer, so my attitude has changed!
I started out last year by buying a cheap Savage .223 bolt "package gun". I gave the scope away, had my 'smith chop the barrel to 19" and he trued the action. I put a medium grade 3X9 on it and it shoots great. My objective was to make a great shooter on the cheap, a gun I wouldn't mind camo-painting, knocking about, etc. The Savage fit my needs perfectly.
In the meantime, one of my buddies had a Rock River AR Varmint in .223 that shoots phenomenally well. He also had been hankering for my Ruger #1 International and a Swiss K-31, so we traded. I just installed a Sightron 3X9X42 with illuminated reticle on it, but haven't done anything else with it yet.
I really can't say that either will be my "ultimate", but I think I have chosen well. The Savage is really light, handy, and accurate. The Rock River is handy and accurate, but it is significantly heavier. Certainly follow-up shots will be quicker with it. I think the Sightron illuminated reticle will be a plus in dim light. I do like the .223 cartridge - usually preferring "standard" cartridges to the hotter numbers like the .22-250. I have always liked bolt actions, but never had an AR. The AR's are so versatile and accurate now that I wanted to try one out.