I work with graphic files for a living so I have to be extremely organized digitally.
The best organization for me is to set up a system of folders. I like to reference item by what they are - So I have a ceramics folder > inside there are several folders > jewery > clay and glass > Cups > mugs > etc. (Some images might be in 2 folders if they fit into both categories - Makes looking for a specific image much easier)
I then have in those folders 2 more folders > Web Images (the small ones) & > RAW images (full size edited)
Any images I do not edit are thrown out. If they are not important enough to edit then it isn't a good photo - It is like choosing what to fire. Sometimes it has to go to the reclaim
I also like to include the month/year when the image was take to the name so my file name might be "BlackMug_Dec2015.jpeg"
I also suggest having a backup - Crashes are real and horrible.
As for editing software I like photoshop because that is what i use almost everyday. But I agree with the editing software that comes with your camera - My sister uses mine and really likes it (she is also a much better photographer than I am)