It depends on what your management objective is. If you are trying to decrease the herd, which is a situation we have been in in the past, you want to shoot the young ones because over their lifespan they will produce more offspring and eat up more food (as will their offspring) than an older doe.

If you would like more deer, shoot the oldest doe because they are closer to being barren, if not already, and therefore not contributing anything to the population. In fact all they do is eat up food that could be feeding younger deer.

If you are content with where your objectives are, like we are now pretty much, shoot the one that looks the tastiest. In other words, the one most likely to drop in its tracks and not taint the meat from lactic acid from an adrenalin rush and running off.