Form 1040-ES - Estimated tax payment

I am a US citizen working within the US as an independent contractor for an international organization. It is my understanding that I have to make estimated quarterly payments. Do I use for 1040-ES? Also, is there a way to file that form through Turbotax. And I would also like to know if I use the Online payment option at IRS website, do I still need to file a form 1040-ES or I can just pay there without filing any forms? I will based my estimated payments on last year’s tax.