A 243 will definitely kill deer cleanly out to 250 yards. Some will tell you that it is on the light end of the spectrum for deer but I have killed a lot of deer with one including my best buck ever last year. The thing about a 243 is that its sort of a dual purpose gun depending on the type of bullet you are using. There are bullets out there for the 243 in low grain weights that are intented for varmit hunting. Unfortunately every year people who don' t know any better shoot deer with these light weight bullets and often get poor results and lost deer. Stick with at least 100 grain bullets in a corelock or some other controlled expansion type round like a nosler partition and a 243 will shoot smooth through any whitetail in America. As for how far a deer will go after the shot? Well that depends on where you hit it. I' ve dropped them in their tracks and I' ve had them run 50 yards or more on occasion. However I have had exactly the same results with my 30-06. Some dropped on the spot and some ran a ways. I have seen deer shot through the heart and lungs with a 300 magnum run a hundred yards before. There is no guarantee of always anchoring one on the spot with any gun (despite what some will tell you) but if you put the bullet where you should with any of the calibers mentioned here a deer won' t go far enough for it to matter.
I own a 243 , 30-06 and a 7mm mag. The older I get the more I lean back towards my 243. I just think that all these big magnums are overkill for most whitetail hunters.