Congratulations on your purchase and welcome to the passion.
I didn't intend for this to be my first post without a proper introduction, but I have been right where you are and I get it.
I would strongly recommend starting fresh and changing all the fluids. I would pull the differential cover to drain it and clean it out. That way you KNOW exactly what you have to start with.
While you have the cover off:
1. Note how many bolts hold it on, 10 or 12?
2. The gear ratio will be stamped into the ring gear.
3. You will be able to identify what type of differential unit you have. If not, posting pictures here will definitely tap into the wealth of knowledge.
4. Once you know what differential type you have, you can select the correct oil and friction modifier you need to run.
5. You will also be able to inspect everything as you go.
Once you know the gear ratio and tire diameter, you can figure out the stall of the converter and its suitability to your application. Heat is a real killer of automatic transmissions. As mentioned above, high-stall converters build a tremendous amount of heat.
That generation TA came with either a 10 or 12 bolt axle. Something would have to be terribly wrong for your 555 to not be producing a lot of torque. However, you don't have a lot of tire. It would be nice if you had a 12-bolt axle for when you step up your traction and actually hook, otherwise that 555 will help you upgrade your axle sooner than later.
That's not to say that you can't enjoy your car without upgrades, it all depends on your driving style and intended usage. If you aren't hammering on it, you won't break parts, but where's the fun if you can't drive it as it was intended?
When you get to the transmission, you probably have a TH400 (Turbo-Hydromatic), but it would be nice to know for sure. If your trans pan doesn't have a drain plug, now is a great opportunity to add one. Maybe even consider a finned aluminium pan, that would help dissipate heat. Just don't go for a deep pan that hangs down and drags on everything.
While you are under your car, look at EVERYTHING. It's good to KNOW what you have and develop a more intimate relationship with your car.
Cheers,
Joe
P.S. If necessary, you can have your torque converter repitched for your application.