I am looking to replace an engine. Do I get the external balanced one or the internal balanced 3.8l?

That has to do with the manufacturing process of the crankshaft. It is difficult to cast two of the counterweights in some designs so they add an extra weight to the harmonic balancer, (vibration damper), and to the flywheel, or in your case to the torque converter. Typically you replace an engine with one like the old one but if you want or need to switch from internally to externally balanced, or the other way around, you have to use the correct torque converter for the engine. Just use the harmonic balancer that came with the engine.

The operating system is engineered for one specific engine and nothing else and changes are not optional.

The car was manufactured in 08 of 1999. Would I be correct in assuming that it has an externally balanced engine in it?

I looked up a few harmonic balancers for your engine on auto parts companies web sites and none of their listings make reference to yours being externally balanced. There is also no visible weight added to the castings that I can see. The easiest way to tell is to look at your balancer. If the engine is externally balanced, you'll see a rather significant extra mass on one side.