Purchase a domain of your choice, then hook it up with a website builder of your choice. Some providers offer both domain + website kit in a bundle. Examples: wix, mailchimp (goes with email marketing tool), wordpress, squarespace, Technically, you could even use carrd for this.
For music in particular use soundcloud, bandcamp, audius, youtube (iirc you still have to use either when you have your own site and want to link to your music). Having an additional site or blog to showcase your work is a bonus.