The most important thing for photo editing is a color-corrected display, such as an IPS display. These provide the widest color gamut, have accurate colors, contrast, and brightness, and would make the biggest impact on the final product. For hardware, it really doesn't matter a whole lot, anything that is current will work with Photoshop. The lower the specs, the longer it will take to do certain tasks such as convert RAW to JPG, but they will work.
For software, I'd recommend Adobe Photoshop or Adobe Lightroom.