I'll personally always recommend Photoshop as a mapping software. It takes a little time to get really comfortable with it, but once you do and combine it with a graphics tablet, there is no limits to what it can do for you. This is also a fantastical place for learning this stuff; I can honestly say that everything I know about using Photoshop today, and I dare say I'm getting pretty handy with it these days, I have learned from the tutorials on this Guild. I knew practically nothing about it going in.
As far as vector software goes, I for one can give a warm recommendation for Affinity Designer. I use AfDe for pretty much all my vector needs and I really like it. I kinda prefer it to Illustrator, it just is less troublesome with some essential little things.
I know a lot of people use the ProFantasy software for mapping, but I've never really used any of those, with the exception for Fractal Terrains which I own for the occasional inspiration boost. So I'm not the best person to say yay or nay on them. Many people do like them though, so I doubt they are too terrible.
My very biased personal view on this, feel free to ignore this PS nut