A professional website is for your illustration work only, and you may eventually find that you need several different websites if you have a variety of styles or fields that you work in. Make sure your professional site is well organized, well designed, quick to load, and easy to navigate. Avoid flashy graphics that slow down and distract your viewers from your work. Keep the site updated with new work while taking down old or outdated pieces. It will look more professional if you buy your own domain name instead of relying on free sites that display advertising.
You may choose to show your work via a commercial illustration showcase such as The Ispot, Children's Illustrators, or a cooperative site like PictureBookArtists.
Do you need a blog?
A blog isn't necessary but if you have the time and interest in maintaining one it can be an interesting addition to your web presence. A blog can also be used as a stand alone website and online portfolio or combined with your illustration website. Post original articles and artwork on a regular basis. Showing the steps from thumbnails to sketches to finals is a good way to show your working methods. Here are some examples of illustrator blogs:
The Dust of Everyday Life
Drawn: The Illustration and Cartooning Blog
DrawerGeek (not a traditional blog but more like a blog of drawings)
Other options for online marketing tools include Twitter, Tumblr, Facebook Business or Fan pages, and Etsy shops. The key to making any of these work for you is to keep your content updated regularly with your new work.