A lot of your choice will depend on what form of competition you intend to participate in. Single shot bolt action handguns can do amazing things, but they probably won't win a bowling pin shoot. .22 RF handguns designed for competition, customized to the hands of the shooter, will print tiny little groups, but won't work as a self defense tool very well. A short barrel 12 gauge will excel at home defense, but won't help if you are trying for the smallest group of 10 shots off a bench. You started out asking for accuracy and worked around to defensive arms. There is no magic combination of gun and caliber that is best in every situation, only the wonderful debate of which is the best for all-around use. If you ever actually have to shoot a home invader, he/she really won't care if you can print a 2" group instead of a 4" group, so long as that group is in the critical triangle.
Maybe you need to decide which power category you are looking at. In formal match shooting, guys try to design a load to just make the minimum power rating for the category in which they intend to compete.
On the other hand, I did a fair bit of informal competition long ago. We shot the National Match course, loading 5 rounds at a time for slow, timed, and rapid fire, in centerfire and rimfire categories. One guy loved his 1911 so much he used it in the rimfire category, his logic being that he could shoot it as well as he could his .22, and the holes were larger, meaning he might pick up a couple of points since points were based on the highest scoring ring your shot cut.