I would suggest a full tuneup first, possibly an MSD ignition system, as the Duraspark system of that era isn't that great. I believe your engine is carbureted, my 83 T-bird was, if so, I suggest you head over to http://www.moranav6racing.com
for a 4bbl Intake manifold and a set of shorty headers.
Hopping up any motor will definitely cost you money, I had a mostly stock 3.8 for a couple years until I swapped it out for a '03 model 3.8 and converted it to carb with a 500CFM Edelbrock, and I love it! The newer motors have significant design differences.
A supercharger on that particular block and head combo is a bad idea because it flows so poorly. If you really want to supercharge it, your look at swapping in a 89-94 Tbird SC motor(Fuel injection, very difficult) or a later model N/A block with adapters. I estimate at least $3000 or more all said and done depending on the route you take.
Feel free to message me any more questions, as I have been dealing with the 3.8l for over 4 years now in a performance aspect.
Check out http://www.V6power.net
for more info on the supercharging and other performance upgrades.