A Form 1099-MISC is required to be filed when payment for services in excess of $600 is paid. If payments are made for a product or to a corporation, a Form 1099-MISC is not required.
Income from part-time consulting would be self-employment income and a customer should file a Form 1099-MISC if payments for consulting exceed $600 for that customer.
Income from self-employment would subject to income tax (income in excess of expenses reported on Schedule C) and Self-employment Tax. If the OP generates as much income as he or she anticipates, withholding would probably not cover the increase in tax. Therefore, quarterly payments can be made using Form 1040-ES (can be downloaded from irs.gov).
There is a penalty under Code Section 6654 for failure to pay estimated tax. This can occur even if you are a W-2 employee and under withhold tax too much. If you are self-employed and do not make estimated tax payments, this penalty can likely come into play. Generally, the amount of required annual installment is the lesser of (1) 90% of the current year's tax or (2) 100% of the prior year's tax. The estimated tax penalty is computed by quarter. Therefore, if you do not make the required annual installment, the IRS will look at each quarter to see if a quarter was underpaid, and if so, how much penalty should be asserted.
Hope this helps.