If you wanted to start an online business with you as the sole proprietor, what tax forms are required on the Federal and State level?

If you have no employees, there are NO forms required at start-up.

If you have W-2 employees, then you will need an Employer Identification Number (EIN), whkich you can get telephonically from the IRS, followed up by the paper-work (Form SS-4, I believe).

You will also have to get a NY state tax ID #.