Traditional paint programs are great for the digital matte look or for photo retouching, but most professional illustrators do much of their digital artwork in vector-based applications.
The advantage to vector drawing is that your illustrations scale; you can shrink or enlarge them as much as you want and you'll never lose quality. The disadvantage is that drawing with vectors takes some practise and some getting used-to, so if you're new to vector illustration you'll have to practise. But once you do, you'll be amazed at their flexibility, their clean digital appearance, and their quality.
Whether you're new to vectors or not, Inkscape has a lot of powerful tools and options that you'll want to get familiar with. A complete course on how to use Inkscape is available for free over at the amazing Screencasters website.