Bob, there's many factors to consider when it comes to what software to try. As Gabby said, Paint.net is a good place to start, but if you want more functionality, you may want to invest in something with more versatility. It all depends on your budget, computer savvy, understanding of graphics, etc. etc......
Some free programs that will get you going:
Paint.net
Inkscape
GIMP
I've listed these in order of complexity/learning curve, but that's my unprofessional opinion! As for OpenOffice Draw, it works, but has very limited functionality compared to the others listed here. Of course there are commercial titles that are even more capable than these, but they've also got a steeper learning curve. There are numerous tutorials online where you can learn to use these titles. As I said, it all depends on how far you want to go with it! Good Luck!