It's always good to stick to industry standards such as Adobe Illustrator. You will find it's basic tools invaluable to create anything you need, but it is also one of those programs that will help you learn more tricks as your projects get more complicated. Vector based artwork is the best tool for creating logos, as you can re-size them to any size without losing quality.
However Adobe Illustrator is expensive. As an alternative, try using a Free Open Source program such as Inkscape
www.sourceforge.org It's multiplatform and complies with a number of standards. Secondly to repeat myself, it's FREE!