Mopar Magnum

What gears should I be running in my rear end? And how can I tell what gears are in it so I can make sure that I am not ordering gears that I already have?

As said by several responders already, we need more info on how you intend to use the car and what is already there. Your Barracuda will perform best with a matched package of components: engine, trans convertor, rear gears, etc. They all need to work together for optimum performance.
The initial pics of the engine look like one of the higher-horsepower crate 360 engines since it has a single-plane intake. Something I haven't seen yet is what make and size of carb is on it or whether the carb is vacuum or mechanical secondaries.
Is the rear end open or Sure-Grip? You can get an idea of what gearing is in the rearend by counting how many revolutions of the drive shaft compared to one complete revolution of a rear tire.
Do a lot of investigative work on the car and post what combo you currently have and what you want the car to be before you start changing components and spending money. Your grandfather must have had friends that possibly helped with the build and may know a lot about the car.
Is your Barracuda going to be a daily driver or just a weekend toy? You have a lot of wide-open space in Texas and won't be happy taking a long-distance cruise with steep gears that are best suited to a strip-only application.
There's a lot of knowledge and experience on this site and we're all here to help one another. Take advantage of it.