Buying a top tier AR from BCM, Daniel Defense, LMT, LWRC, Larue, Colt and the like are great battle rifles. For building a coyote rifle, you can do a better build for hunting than battle. I have built many lowers on Aero Precision lowers, uppers, handguards etc... I like Aero for their lower parts kit.
Like cactusjack says, dont buy cheap stuff. It will bite you more times than not. You can trust the top tier companies for parts and stuff, but you will pay a higher price. Aero makes good stuff and they make a bunch of lowers and parts for other companies too. You can watch youtube and there are many how to videos and you can easily build one from ground up.
Hunting barrel I would do a wylde chamber in a 18 inch in 1:8 twist. AR15 Performance makes some good quality and good cost barrels. Bison Armory makes great barrels but at higher price.
stripped lower - 75
or buy complete lower with ready to go for about - 230
complete upper - 70
Lower parts kit - 70-100 not including buffer tube, stock
Or lower parts builder kit for about 120 includes all the above
handguard - 200
barrel - 250
gas tube and block - 50
total - about 800 and you can do that just with buying Aero Precision
