I have never used a .243 so I can not comment on what grain or style of bullet you should use, but a double lung will take a deer out, if you know your gun has the power to do it a broadside in the shoulder will take them out also, they do not run with both shouders broke and usually both lungs are blown also, I still prefer a double lung shot because it is a garuanteed humane kill and you waste less meat.
The Tazman aka Martin Price
Founder and President of
Virginia Disabled Outdoorsmen Club