One luxury of this field and getting to meet a lot of talented, creative people. The problem, their websites typically suck. So I thought it would be worth mentioning what the common problems are and some solutions.
Invisible Design Myth
I think when artists begin planning their website, they want their work to do most of the talking. Which is fine. However, I believe they often go with a minimalism design thinking with less there it won't get in the way of their work. The problem is, it doesn't matter how few elements you have in a design, if they're not used to emphasize the content correctly, it will always distract from it. The result is like putting street at in the Luvre in Paris. It just doesn't fit. When a design is made to enhance your content, and as a part of your content, it doesn't draw attention to itself, it just becomes a unified experience for the user.
Expression vs. Communication
Another common issue I see with artist sites is that they want to express themselves with their site. Which of course is what makes for good art, but a website is a design, it's a vessel, it's a tool, it gives people understanding of who the artist is, and what their work is about. It's value is determined what it offers everyone but themselves. That said, a bit of self expression can aid in the communication of who the artist is. Much like the approach I took with my logo.
No Actionable Direction
The biggest issue I have with artists' sites is there is nothing to do on them. Check out a few of their works, read a few blog posts about them then what? There needs to be a action the user can follow up with like getting in touch, ordering a print, commissioning them for an original work, seeing their gallery exhibit. Something the user can do to be involved.
Software
I've seen a lot of artists go for a pre-made solution, especially on an "artist network". The problem with this is that you lose the potential to create an identity for yourself, your site just becomes network site #739. I would recommend a self-hosted WordPress site with a custom theme and a original domain. The only part of your site that is streamlined is the system you use to maintain it. It will be easy to find a front-end designer to make a theme for it, or a brand-able premium theme for a decent price. Another nice advantage is that WordPress can grow with you. Want a shopping cart? No problem! Want a blog? No problem! Want to change how your gallery system works? No problem!