I’m lucky enough to build WordPress websites for an über talented design agency that has a number of musicians on their books. I take their beautiful designs and build them into websites, and whilst all are completely different, they often use the same WordPress plugins for essential features.
For a free plugin, Gigpress rocks. It allows you to add in as much or little gig/tour info as is needed, date, venue, address, map location, link to ticket sales website. It also comes with a number of shortcode options so you can display gig info in pages and posts as you need, for example you might want to automatically list the next 10 upcoming shows on your homepage.
Soundcloud is a social sharing platform for musicians/sound creators. Use the Soundcloud Shortcode plugin to easily add in any track that has been uploaded to Soundcloud in a page or post:
Photospace runs off the built in WordPress gallery and is a really slick way to show off your photos. Photos are uploaded to the page and the gallery is displayed by with the [photospace] shortcode. Really simple and neat, I love this plugin.