I have two that qualify. One is a Remington 7400; mine is in .270 Win and is MagNaPorted. The other is a Browning BAR in .30-06. Both of these rifles were set up for hunting whitetail deer in the brush and thickets of the Northeastern US. Each is fitted with a 1.5x5 variable power scope.
Both of them shoot accurately enough. The Rem is a little loud, but the barrel barely jumps at the shot; follow-up shots are quick!
The BAR is easily the softest shooting 30-06 I have ever fired. The Rem is about $100 or so cheaper than the Browning; the Browning has a wider selection of calibers including magnum calibers.
I also have M1 Garands and various other military style semi-autos, but don't truly consider them to be "hunting" rifles.
Good luck with your choice!