About free GIS software, I recommend you from my experience gvSIG software (TRANSLATED TO LOTS OF LANGUAGES) or QGIS too, both are very good. I leave you here the links to both sites where you can download them and try. Im even doing my Ph.D. studies with gvSIG and it going on well.
http://www.gvsig.com/en/home
http://www.qgis.org/es/site/
About digital retouching programmes, I use photoshop for my maps, but I have also used Adobe Illustrator, and its goog too. I know for some colleagues, they use Freehand, but cant tell you how it works.
Ok, to make it easy and free :-), download QGIS - free and open source - you can get it at http://www.qgis.org/en/site/ with lots of language mutations...
data can be downloaded (again free and open) at: http://www.naturalearthdata.com/downloads/ or http://www.diva-gis.org/Data
As an 'alternative' to free ware, if you would like to practice with ESRI ArcGIS, the student licence (or for any private, non-commercial use - 'ArcGIS For Home Use') is only $100 for one year.
According to financial condition, people can use ArcGIS(not free) or QGIS(Free),
I idea is, if you ride a bicycle in BSA, why not in other brand. but learning curve may be little difficult in free software. Initially in the year 2002, I learned GRASS with RedHat, I conducted open source GIS training in IITM, chennai, Inida (April 2009). They appreciated. all the best.
Software is only part of the process, and you have many to choose from. Please also consider how to make a good map. Apologies if these are already things you know.
For starters, do not use a geographic coordinate system (latitude and longitude) for your map, select an appropriate map projection: