Being an online mobile app, Hangouts uses only data (your bandwidth) to make the calls, not your actual telephone line. As per this Google support link, calls to most destinations in USA and Canada are free of cost from Hangouts so you shouldn't be billed anything (but you will be billed for the data/bandwidth used, of course!)
The exception is a few rare locations mentioned in that link that cost 1 cent per minute. And those calls will not be billed by AT&T, to pay for those calls, you'll have to purchase Google calling credit from here separately.
Or will hangouts first check if this contact has a phone number associated with it, and instead use that.
You can either dial a number directly, or if you have that person in your Google contact list, you just type the name and number will come automatically. Even if the person doesn't have a number, Hangouts will work and you'll be able to make the call since that contact's identity will be based on the Google account, not their telephone numbers (check the Making a call with Hangouts section in the referred link). Google is all about seamless communication!
But what I don't understand is why are you paying for both a data plan and talktime to AT&T? As per the support link, US & Canada calling is mostly free from hangouts, so if you already have a data plan, I don't see any need to buy that sim card for "making calls at a reasonable price".