First - get a professional tax consultation with a NY-licensed CPA or EA.
At what point do I need to worry about collecting sales taxes for the city and state of New York?
Generally, from the beginning. See here for more information on NYS sales tax.
At what point do I need to worry about record-keeping to report the income on my own taxes?
From the beginning. Even before that, since you need the records to calculate the costs of production and expenses. I suggest starting recording everything, as soon as possible.
What sort of business structures should I research if I want to
formalize this as less of a hobby and more of a business?
You don't have to have a business structure, you can do it as a sole proprietor. If you're doing it for-profit - I suggest treating it as a business, and reporting it on your taxes as a business (Schedule C), so that you could deduct the initial losses. But the tax authorities don't like business that keep losing money, so if you're not expecting any profit in the next 3-4 years - keep it reported as a hobby (Misc income).
Talk to a licensed tax professional about the differences in tax treatment and reporting. You will still be taxed on your income, and will still be liable for sales tax, whether you treat it as a hobby or as a business.
Official business (for-profit activity) will require additional licenses and fees, hobby (not-for-profit activity) might not. Check with the local authorities (city/county/State).