In my case I had an old family photo but had no idea who the people in it were. In February of last year I found out they were my great grandfather and his daughters. So I had to get the photo repaired. I then discovered my laptop had come preloaded with a dodgy years old version of Photoshop Elements (that’s the non-professional version). So I set about learning it so I could repair my photo. Then my hard drive crashed taking the dodgy PE with it. I tried Gimp but I was by then too used to PE so I bought a new version of it (Aus$120).
As Andy says there are plenty of competing programs, basically with similar tools, set up in different ways. Think of it as like being a carpenter, in the end it depends more on the skills and styles you develop than the brand of tools you use.
I think I’m slower than Andy. I took over an hour on your photo, mainly trying to get the damaged eyes right.
And, again as Andy says, it becomes very addictive. Ever since I worked on that photo of my relatives I haven’t been able to stop!
Cheers,
Peter