I know you don't want to consider an engine swap. I still think you should, though, because the first step in high performance is a fresh engine. It's fine if you want to stay V6, or even 3.8 V6, I just think you should rebuild one and put your performance stuff on it. I hate having the engine out of the car and the car not moving under it's own power. If you rebuild a second engine in the garage, you can swap it in on a Saturday and then you're up and running in no time!
That being said, you can do 3.8 V6 engines just like any other engine. Once you are SURE that your bottom end can take the power, you go to the intake/heads/cam/exhaust scenarios and then pick or modify your carb based on those first selections.
You must buy at least one "building a Buick V6 engine" type book. Even in stock form there are oiling system mods that must be done to ensure the long life of your Buick engine.
Start with exhaust. First, you need headers. Next, you want 2 1/4 (I have also used 2 1/2 with not much difference or loss in bottom end) pipes off of the headers. You can either put those into a nice y-pipe (like a flowmaster 2 into 1 y-transition) or you can run duals. If you run a y-pipe then run a 3" cat-back setup that flows nicely. With duals, you just need good turbo mufflers, or whatever aftermarket muffler brand you like best.
Next, you need to pick the cam for the power level you want. There are many to choose from so do lots of research.
After you pick your cam, you need to modify your heads. Port/polish in the bowl area with a 3 angle or 5 angle valve job is a must. You can polish the exhaust to mirror smoothness, but not the intake ports. Just gasket match the ports to the gasket and do a little smoothing on the inside to get rid of the casting flash on the walls, floor and transition turns. You want some roughness inside that intake port to help break up the air/fuel mixture as it heads for the intake valve. You need high lift valve springs, and you may have to have the heads modified to accept them.
Gasket match your intake. You should have purchased an aftermarket intake by now and all you need to do is gasket match the ports. With the ports in your heads and intake gasket matched, but not enlarged, you will maintain excellent port velocity. This is important when building a naturally aspirated engine.
Last, fuel delivery. Your car is running a wet manifold system. You could buy an aftermarket carburetor, modify your stock system, or convert to a TBI system from a 4.3 chevy V6. I have done it and was VERY happy. You will have to tune the computer if you want it to be perfect. If you stay carbureted, I would start with a bigger two barrel or a small aftermarket 4bbl, like a 390 Holley.
Good Luck!