Mapping software solutions, there are a bunch, it really depends on the way you like to work, how much time you have to learn, what your budget allows and your goals.
Many members here are Profantasy Campaign Cartographer users CC2, CC3, Dungeon Designer, City Designer and more. These are CAD programs and completely different than standard graphics applications.
There's also Dundjinni which more of a combat scale battlemap maker, not good at regional/world mapping. As well as NBOS Fractal Mapper.
There proggies cost around $40 each.
GIMP is the open source version of Photoshop, Inkscape is the open source version of Illustrator - which basically means that most any vector drawing app and/or raster image editor works great for creating digital maps.
Some prefer CAD, some prefer vector or raster apps - it really depends on you, there is not a single package that is best for all mappers.
Explore this site, look deep, there are many samples, tutorials and discussions about all these apps. Read them, try out the free ones, or splurge on one of the low cost paid-for apps and start mapping.
That's my advice!