Don't know much about hunting deer in Texas, but I presume its about the same every where, with the exception of laws that apply in your area. I suggest stay hidden downwind of the deer you plan to hunt, and shoot straight for a good clean kill.
If you can get a standing still, broadside base of the neck shot, take it. It will drop any deer in its tracks. Aim for center of neck at the base. Make sure your rifle is zeroed in at least for a hundred yards, and you will be able to hit anything out to 200 yards.
If you choose to shoot at a running deer, do yourself a favor, and pick a spot ahead of the deer, and wait for the deer to get there. It makes for a much easier and surer shot.
Hope this helps.