Procedure to start ecommerce business
You will have a few options to consider, depending on your business plans. To start simple, let's begin where you are, in New York City:
Typically, an LLC is the best choice with e-commerce sites that have 1 to 3 owners for it's flexibility and simplicity. In New York State, LLC's can be very expensive due to the state law requiring new LLC's to do newspaper publications. This presents a choice to either handle the publications requirement (you must publish a notice of company formation in 2 newspapers for 6 consecutive weeks), or you could open an S-Corp, which is a corporation that elects to be taxed as a small business, very similarly to the LLC's structure as the income is passed-through directly to the owner's personal income.
If you don't have any physical connection to New York (such as an office, employees, warehouse, etc), you may want to explore the possibility of registering your business in a more business-friendly state, such as Delaware. The state of Delaware does not charge a state sales tax, so your business wouldn't have to get that permit to be able to sell products as you would have to in most states.
Please take a few minutes to read through the differences between an LLC and an S-Corp. With the aid of an accountant, you would be able to come up with the best fit and strategy for your specific situation. You could always form a standard C-Corporation, however, the tax structure of a C-corporation is not usually best for smaller business owners.
Once you know what state and entity type fits your business the most proficiently, then you would have to file your business applications with the appropriate state and the IRS.
I hope you found this answer to be helpful.