Are you shooting in RAW? If not, the power of Lightroom, Capture One, etc. will be largely wasted on JPGs. Shooting on Auto on the camera doesn't really negate post processing of RAW files or not, though if you are happy with the colors and exposure of the JPGs straight out of camera then I'd say keep doing what you're doing. What aren't you happy about with your current photos? Some things are a byproduct of sensor and lens combinations vs. post processing and no software will be able to really help depending on what it is. As mentioned above, depending on what kind of corrections you are looking to do there may be free, simple options for software, but if you are looking at doing heavy editing of RAW files with masking, presets, lens corrections, etc. then something like Lightroom or Capture One will be what you are looking for.