1. Just learning how to shoot pistols, primarily for plinking and fun at the range.
.22 long rifle handgun (either autoloader or revolver, doesn't matter) fits that one perfectly. There's no getting around the logic of the cheap ammunition, nearly nonexistent recoil. Perfect, easy way to practice and master trigger control and the fundamentals of shooting.
2. First gun, needs to cover ALL bases, including hunting and defense until the funds are available to get more specialized weapons.
.357 Magnum revolver with 4" barrel. Long-since proven man-stopper, and also a long-since proven whitetail round. 4" barrel models are usually still small enough to be carried concealed. And they can chamber and fire .38 special rounds for lower recoil during practice.