Kinda depends on how far you'll be toting the rifle to hunt said yotes. Just 50 yards from the pickup or 4-wheeler, or humping it a ways? If the latter, then a lighter rifle.
As for chambering, .243 win and .22-250 are popular large varmint chamberings for good reason. But a .223 rem rifle is a good choice, too, and there are dozens and dozens of choices in this caliber.
Does the $700 include or not include scope, base, rings, tax, FFL, shipping, sling and/or ammo? Willing to buy used, or new only? I can think of few better "yote rifles" than my T/C Icon "Original" in .243 Win, but with optics and mounting hardware, it came in a ways over $700, even used.