I like Paint Shop Pro. I find it easy to use and it does pretty much everything I want from it. If you can get a cheap or even free copy of PSP x8 you will find it is the most stable of them all and a great start.
Aftershot Pro 3 ...... Well, I have never been able to see what benefit it has over others. Personally I don't like the results I get from it. You would be much better off getting DXO or another program which I'm sure others will recommend. (I splashed out on Capture One when it was 25% off that is still very expensive but it really is the best IMO)
I have been using PaintShop Pro for over 20 years and like it very much. If you need a powerful, layered image editor, it is the best bang for the bucks, IMHO. I think Affinity Photo is also a good choice, but I am so used to PSP that I'm sticking with it.
As far as Aftershot Pro 3, it is a raw file editor, so it is not the same as PSP (so it's not "and or", it's "and"). I liked it OK when I was using it, but prefer the opensource program Rawtherapee. Aftershot is more user friendly certainly, and a very good raw editor, especially if you can get a deal with it bundled with PSP.
PSP is very good value for money and quite powerful. Does layers and most editing functions. HDR is is not great in it and does not do focus stacking (although I'm a few versions behind). That is the other advantage (or maybe disadvantage depending on how you look at it) you pay for a license once and that's it, no annual renewal fee. It also accepts plugins. I have all the Nick add-ons as a plugin (the original free version) and a few TOPAZ plugins, Topaz Denoise AI and Topaz Sharpen AI.
Also upgrade is fairly cheap. I'm thinking of upgrading to next new version as it has a few features that my older version does not have.