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. You can also point your domain name (e.g. alextheartist.com) to .Mac, so people won’t see that the real URL is gallery.mac.com/alextheartist.
Also, you can design your own site with a program like RapidWeaver. Hosting a web site can be as cheap as $4/month. I have yet to find a reason to go somewhere besides GoDaddy.
…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.