Well, first off, I must say welcome the the guild, the mappiest Place on the web.
Secondly, you should have a peek at the Quick Start Guide stickied at the top of this forum. Nice tips for starting into mapping.
thirdly, if budget is formost on your mind, I would suggest downloading GIMP (it is free) and then jumping into some of the gimp tutorials that you can find in the Totorials forum. You can find that further down on the main forum page. Look for the Creating a Regional Map in Gimp, by RobA. This tut will teach you GOOOOBBBBBSSSSS of techniques and is a great intro into the program. There are many other tuts that you could look at, but that one is loaded with stuff for the beginner. Once you have tried it a few times, look at the others and start working on you own style.
Fourthly, As soon as you start a project (also called a Work In Progress) post it in the appropriate WIP thread. This way you will get plenty of constructive critiques and comments along with help for those times that you get stuck on something.
And Finally, have fun and enjoy your stay