$500 for the bare rifle? And then add the $ for scope, sling and mounts? Plus $ for ammo?
I'd haunt a gun store, regularly, looking for a recent trade-in. If you're Johnny-on-the-spot, you can sometimes get a great deal. Or, check out a gun show or two. There are a lot of good buys for rifle and scope for $500 or less.
If you are watching the pennies, and want only a NIB gun, the Savage 110 is the least costly and has had almost exclusively good comments here on TFL.
Wally World gets around $365 plus tax for a 700ADL, plastic stock, but I've only seen them in .308--so that's a "dunno". I have one in .308, and am still trying to get it to shoot as well as a .308 sporter should.
If the cost of a Leupold is a bit much, an older Simmons 44 Mag is a decent scope. I'm told that those made in the last couple of years are not as good. I haven't heard any squawks against Burris.
I've been using Weaver and Weaver-style bases and rings for 50 years; they've always worked quite well.
The Federal 85-grain HPBT loads work quite well on coyotes, and I've taken some 20 whitetails with that load. Most of my deer were well within 150 yards; mostly either heart or neck shots.
FWIW, Art