Straight answer

Do I need an ESTA for the USA?

Yes, every traveller needs one, including babies. You apply online before you travel, it is valid for two years or until your passport expires, whichever comes first, and there is a fee per person. Two warnings from experience: apply on the official US government site, not the copycat sites that charge extra for nothing, and do it as soon as you book rather than the week before, because a refused ESTA is far easier to deal with three months out. If you have visited certain countries or hold certain dual nationalities you may need a full visa instead; tell us and we will point you at the rules.