Artists interested in trying their hand at digital art are sometimes confused about what software programs to buy. With good reason. There are lots of packages out there and it is wicked confusing. Unfortunately, there is no one software program that I can recommend that you start with. It really depends on you. My advice would be to look at digital artist's and work and see what speaks to you. Then find out what software they use. Of course you don't want to copy anyone's work, but you will have a better idea of how you want to transition into digital art.
That said, let me introduce you to an artist that uses Adobe Illustrator. The above illustrations are by my friend Jannie Ho. Using Illustrator she creates colorful children's illustrations that are slightly wacky and really adorable. You can see more of her work at www.chickengirldesign.com.