Thanks for the suggestions, folks! With a little research, I quickly realised that a Chromebook would be almost useless for what I want to do (partly because of its modest RAM, mainly because of its low-resolution screen). Oh well ...
GIMP is fun. I think the biggest thing will be learning terminology, some things are just called differently in one than the other.
I've downloaded GIMP 3.0.4. onto a borrowed laptop (Win10) but I have yet to hit "fun"! Since much of what I do begins with the removal of the background, that is what I started with on a trial image. Oh dear!
In Photoshop, you outline part of the unwanted background by playing connect-the-dots with the Lasso tool. Then Control X to cut out that part of the image (leaving, in my case, a white background). Then Control S to save what you've done thus far in psd. Then repeat until you've eliminated as much of the background as you require.
I tried to do the same in GIMP. I was selecting the first area to cut out using the Free Select Tool. As I proceeded (after 3 x clicks), the selection suddenly snapped to a reduced area. I thought 'close enough for an experiment' and Cut. As desired, the selected area turned to background white ... but all around that cut area looked like it had been airbrushed at a fuzzy, low-pressure setting.
Looking around at tutorials, I realised that one must 'commit' Free Select Tool before cutting. I did. Same result. Then I tried deselecting Anti-Alias and Feather Edges separately and then together. Sames results in all cases. After turning Anti-Alias back on, I shut down GIMP and started again. The bold fuzzy outline is now replaced by a subtler 'airbrush' effect ... but it is still there.
So, am I missing something here? Embarrassing to stall on Step 1 of GIMP! But, thus far, very little seems intuitive to me ... and, yes, I am aware that I am whinging about challenges with
free software
