It sounds like you have Wifi already if you are watching on your laptop.
If already you have Wifi, either via a hotspot or whatever, that part of the equation is solved. You will churn through data so it's recommended you get a good unlimited plan.
A firestick is nothing more than a wifi receiver that plugs into your TV that you can load apps to. Amazon Prime just happens to be one of those apps. You plug the firestick into the TV and select it from the input menu on your TV just like your antenna or cable. On our Firestick we have Prime, Sling, Apple, etc etc. Most apps require a subscription but that's beside the point from a technical perspective. If you have a smart TV you can forgo the firestick and load apps directly to your TV as smart TV's already have a wifi receiver built in. I still like a firestick though because it's portable and I can plug it into any TV with an HDMI port. Home, hotels, visiting friends, the rv, etc. Portability does not eliminate the need for wifi though. Having a receiver for content is one thing. Having wifi to get it to the receiver is the other.