Your side business can be organized in several ways, the simplest is self-employment filed on a Schedule C. Regardless of how it's organized, you'll record valid business expenses and business income and come to your business profit or loss. Losses will offset ordinary income (from your full-time job), decreasing tax liability. In the case of assets that you are purchasing, you don't count the full purchase as an expense at time of purchase, but rather depreciate them over their useful life, so maybe you pay $1,000 for your guitar but take $200 in depreciation each year for five years, the idea behind depreciation is that the guitar is an asset that has value even after being used. You can research Section 179 which essentially enables businesses to depreciate the full amount of an asset in the first year.
The IRS differentiates between hobbies and businesses. A hobby can make money, but with a hobby you can't use losses to offset ordinary income (they still want tax on profits of course). Generally, if you are trying to make money at the activity and function like a business, the IRS will accept the business classification. You'll frequently hear that you have to show profit 3 of last 5 years to be considered a business, but that's not true, you can lose money every year and still be a business. However, if you have profit 3 of last 5 years the IRS presumes you are a business, which means they are less likely to audit to see if it should be considered a hobby. Here's a section of considerations the IRS uses in determining hobby vs business:
- Whether you carry on the activity in a businesslike manner and
maintain complete and accurate books and records.
- Whether the time and
effort you put into the activity indicate you intend to make it
profitable.
- Whether you depend on income from the activity for your
livelihood.
- Whether your losses are due to circumstances beyond your
control (or are normal in the startup phase of your type of business).
- Whether you change your methods of operation in an attempt to improve
profitability.
- Whether you or your advisors have the knowledge needed
to carry on the activity as a successful business.
- Whether you were
successful in making a profit in similar activities in the past.
- Whether the activity makes a profit in some years and how much profit
it makes.
- Whether you can expect to make a future profit from the
appreciation of the assets used in the activity.
Note that this list is not a set of criteria that you must check off to qualify your business, it's just the questions they think through in making the decision, just because it's a side-business and you don't rely on the income doesn't mean it's not a business.
In my opinion, keeping thorough separate business records and engaging in some form of advertising would a great way to prove that your band is a business, setting up an LLC or Partnership and having separate business bank accounts would be wise too.