What is the best place for me to do a website for my artwork?
As usual, there’s free…
Post images to a photo site like Flickr.
There are multiple benefits to this approach: easy slideshows, easy “tagging” (e.g. ceramics, painting, installation)
… or cheap…
Apple has the .Mac service for $99/year. You can look at all the features — it’s pretty useful, especially when you get a laptop, but just for example, here’s one of my web galleries, and one in a different style. One posts all the images straight out of iPhoto.
…and not cheap: hire a web designer …
This is doable, but for many folks, let’s just say a cost/benefit analysis would not favor this approach.
I know that, many times, a gallery who represents you will post the work that you have given them. Finesilver had some nice-looking pages.
Finally, I would suggest googling a bunch of artists you dig, see whose web sites you like, and asking them how they did it. FWIW, I just looked up Lloyd Walsh off the top of my head, and he used .Mac for at least a few images.
UPDATE 2013-04-03: Apple’s services .Mac, later MobileMe, don’t exist any longer, and their successor iCloud doesn’t offer web galleries. I recommend SquareSpace for all web-publishing needs. WordPress is certainly a viable platform still, but SquareSpace is much more configurable and user-friendly.