Welcome. I'm going to suggest using Photoshop to start and maybe bring in Gimp if there's something it can't do. There's no reason you can't use all three together, to their own strengths. BTW, Painter does have layers...they 're just not as versatile as those in the other apps. I've never used Painter for maps but I bet somebody like Djekspeck, an awesome cartographer here that often does maps by hand, could turn out great stuff with it. It all depends upon what styles and techniques work best for you. Try some tutorials and get a feel for the apps.
M