The Sierra #1370 63gr Semi-Spitzer, Winchester 64gr PowerPoint and Nosler Partition 60gr all have a good track record on deer and in 1:12" twist 223 H&Rs. Let me add that if the barrel is a 20" Superlight, it needs to be shot cool, or groups will not be satisfactory.
Be sure to read the Handi Basics 101 sticky too, there are some simple things that you need to be aware of that will make or break accuracy in an H&R.
Tim