You don't need to "buy" a trademark.
You create a name (and/or logo) to use for your products or services. You identify your products or your services with this trademark and you gain rights to the mark through the use of it in commerce - through the marketing of your products and services to the public. The public identifies your goods and services by your trademark (ie, you know a Coke is a Coke because of its trademarked name on the can).
You can register your mark in your state or federally, but registration is not a requirement. It is, however, added protection for your mark. Federal registration is notice to all others that the trademark you have chosen to identify your products or services is being used. It is public notice that your mark is taken.
Registration also provides you with the presumption of ownership, so that you can (potentially) prevent all others from using the same or a similar mark to identify their goods. In the U.S., the "owner" of a trademark is (generally) the first to use that particular mark in commerce and not the first to register a mark.
Therefore, once you start using your mark to identify your music and your teeshirts and your paintings and whatever else you wish to market, you have rights to that trademark for those goods (if you are the first to use the mark).
An example: I have a band named "SuperBand" and I market my music under that name. I also sell SuperBand teeshirts and SuperBand posters and mugs with the trademarked name "SuperBand." No one else can market music or teeshirts or mugs using my SuperBand trademark without risking an infringement action. The mark belongs to me. I can register the mark to provide notice to the public that the name is in use.
See
http://www.uspto.gov, the U.S. Patent and Trademark Office website for more information on trademarks and on registering your mark.
Again, all of this is assuming no one else currently has the same or a similar mark to the one you plan to use to identify your music and products. You should check to make sure the trademark you have chosen does not infringe on any other.
Good luck.
