think of the type of hunting you are actually going to do and that'll pick your rifle for you.
many in and out sets on coyotes? usual sets are big walks in and out? probably a lighter weight sporter profile rifle will be better to hump in and out.
lounging a round on a set or 2 a day waiting for something to show up? you can get away with a heavier barreled / stocked rifle, but it's still a pain in the ass to hump around.
brushy, wooded areas or open spots mostly hunted? a combo of both? a 20" inch or shorter is very handy.
for an off the shelf budget rifle(s) my vote is tied vote with howa SA, 20" already set up with scope, a hogue stock, 1 piece base, 2 stage trigger although a heavy barrel, it is somewhat balanced well
Legacy Sports - Hogue Targetmaster Package it's over your 500.00, but it comes with everything you need / want except for ammo. could even bolt on an affordable DBM from howa (though having stuff hangin off your yote rifle tend to hinder
rather than help)
tied for the top a stevens 200 for around 350.00
Savage Arms cut the barrel back to 20 or less. no guilt if you beat it up alittle, and accurate as hell. lightweight too.
if you can wait till black friday, dick's should be doing the rem 700 varmint again for around 400.00. heavy and unbalanced, but accurate get it cut to 20" or less.
.243 for yotes, groundhogs and such, and is beefy enough for deer and those hogs you got down there in 'Bama.
or even 25-06 mdl 11
Savage Arms
.308 is another overlooked choice, 110 gr vmaxes and the ability to load subsonics heavy bullet easily.
also dicks has a savage 11 vt that is tacticoolish for 500.00 or under, heavy barreled and heavy rifle in general, get her cut to 20" or less too.
out of all of them, for real world hunting, a short & light rifle pays off better in the long run. any of the above will talk by the amount of fur, venison, and pork they'll put on the ground.