Hunting ethics and safety
Welcome to the hunting world! The most important things in hunting are safety and ethical hunting.
Don't shoot a deer just to shoot a deer. If it is not a good shot, don't take it. Know the limitations of your shooting abilities, the shooting abilities of your son, the limitations of your caliber/bullet and the weather conditions (wind drift, etc.). Be aware what is beyond your target. Shot placement is important with all calibers, but especially with a 243. You do not want to track a wounded deer. Also be aware of the proper hit zone(s) for the type of shot you are offered. If the deer is small and there is little meat, pass up the shot. See if you can find an experienced hunter/rifleman who is willing to work with you and your son. Be sure to get permission for that person to also be hunting on the land.
I would prefer that you and your son be in a tree stand and not on the ground. This will get both of you off the ground if someone takes a shot at a deer that is heading towards you. It is also safer for the shots you would take, as the bullet is aimed towards the ground. Be sure both you and your son use a properly fitted safety harness. Never climb up or down a tree stand with a loaded gun. I always unload my gun, put it in a thin fabric case and attach a cord to raise and lower the gun. Make sure the gun is unloaded.
Hunting is a great way to teach patience. Teach your son to appreaciate what God has made in nature.
You have been given some very good info in the above responses like making sure both of you are comfortable and warm. Also make very slow movements with all of your body parts (head, arms, legs and torso). If you so shoot a dear, wait about three to five minutes before you leave the stand. Is is possible for the deer to get up and run off after going down. Always approach a downed animal from the rear. Use a stick (preferred) or the muzzle end of the rifle to poke the animal in the buttocks.