Your various social networking profiles can never take the place of having your own music website. When you have your own artist website, you have complete freedom to control the message and create a recognizable "brand" for your music. Think of labels like 4AD or album covers from bands like The Smiths—you know them as soon as you see them. With your own website, you can create a similar association for your fans with your music.
That's all well and good, of course, but there are certain things you need to have on your website to get the most out of it. By that same token, there are things you should definitely skip. Let's take it from the top:
Things You Should Have on Your Website
Well, duh! Your website should have a place for people to listen to your music and links to places people can download your songs. If you are selling physical copies, have an order function—Paypal will do the trick—so people can order your CDs directly from you.
Have a way for fans to contact you and a way for press/promoters/manager/other industry people to reach you. If you have a PR company, a manager, a label or so on that should fielding certain requests for you, then make sure their contact information is there as well. It is really important. If you have, say, an agent and everyone is contacting you instead of them to book shows, it creates a lot of confusion.
Background information gives your fans a chance to learn more about you, of course, but when you have your bio on your site, it gives members of the media an easy way to research your band in one easy step which makes them more inclined to write about you/write longer pieces about you.
Whether you call it a blog or a news section, have one part of your site that receives regular updates. It is where you can announce new releases and tours, but it is also where you create a more personal connection with your fans. Tell them about being in the studio, write about your new favorite song—anything that gives them a glimpse behind the scenes. Be sure to keep this section fresh. "Last update: Nov 2015" is not a welcoming sight to see.
First and foremost, have your press photos on the site, and have a downloadable version that the press can grab and use in their publications. It is the most important thing to have. Beyond that, it is up to you to what extent you want to add candid photos to your site. Shots from backstage at your shows, in the studio, and so on can be fun for fans to look at.
Post links to your various social networking profiles—this is a must. Beyond those links, links to your label, your favorite musicians, and so on are also good choices. Any site you like that you want to share with your fans is fine to put on the list, though putting up sites that are pornographic or that advocate violence probably are best kept to yourself (and yes, I say this because I have seen musicians put these links on their sites).
Whether it is a comment section in your blog, a forum/message board or something else entirely (or all of the above), make sure your website provides a way for fans to leave you feedback. Your fan feedback will tell you what is working, what isn't, and what your fans want that you're not delivering.
Now, naturally, you should have fun with your website, and you can add games and other features as you see fit. This list above simply details that must-haves. Likewise, there are things—like a discography—that become appropriate after you have been working at things for a while and have a longer history.
There are some things to avoid on your site.
Things You Shouldn't Have on Your Website
OK, we all make typos. I happen to be something of a queen of such mistakes. However, do your best to catch them and pay special attention to words that are associated with your music career. What I'm saying here is: don't be "songwriter." Use a spell check program and encourage your family and friends to set aside concerns over your delicate ego and point out mistakes that you have made.
Consider this the MySpace/Twitter profile problem. Just because you have decided that you have a record label, say, don't call yourself a "CEO"—a CEO is a real job with a very specific definition. Don't claim to be signed to a major label when you are an unsigned artist. Not only do people see through those claims, what is the point in telling people who may be able to give you a record deal that you already have one? Ditto for outlandish sales figures, doing the pretend-jack-of-all-trades routine ("I am a musician/model/film director/actor" when really, you've never professionally done any of the above), and other self-anointed titles. You may think that giving yourself a resume boost or talking a big game will lead to bigger things, but the opposite is true. It makes you look a bit silly and uninformed about how the industry works, plus it makes you look dishonest. None of these are attractive traits in a potential business partner. Honesty—it is more effective than you think.
If I can stop just one person from typing lIkE tHiS, then my work here is done.
No, that photo of you leaning over, wearing next to nothing, that you snapped in the mirror using your cell phone does NOT belong on your site. Trust me.