I have a 99 Firebird with the same engine, minus the supercharger, and I really like the Pennzoil High Mileage 10W-30 I'm running in it right now. It worked great at slowing down a slight leak it had and it sounds very quiet as well. I've driven the car in a few cruises (stop and go for many hours at a time with jack rabbit starts and some aggressive driving/revving/etc.) and it's held up great. I tried Mobil 1 High Mileage 10W-30 before this and performance wise it felt the same, but it did absolutely nothing for the leak. Plus, the Pennzoil is over $5 less per jug.
Edit: forgot to mention that in 1999, GM recommended 10W-30 for these engines. I'd go with that.
Unless you have a coolant leak, the engine is so easy on oil it probably comes out cleaner with the right filter. Check the oil cap and see if it has any sludge in it. Change the PCV valve, SC oil, valve cover gaskets, coolant elbow, and drive it.
10w30 was recommended for them in Aus too but a lot of people here also run 15w40 or KMart 20w50 in them without any problems haha
Personally i like anything within the 5/10w30/40 range and will be perfect in any engine of that era
For South Cal., any 5W/10-30 will be fine. My 3800 SC seemed to like QSUD the best as recommended to others. Good recommendations above.
Also read many good threads off the GS forum to complete maintenance to struts, air shocks, serpentine and supercharger belts, supercharger and other projects on my PAU.
We always used whatever conventional 10w30 that was on sale for when I had my old 3.8 GM. Never gave me problems even in 10* PA mornings. Even ran 10w40, but it was sluggish with that. The 3400 we have now seems like it has more valve-train noise with a synthetic 5w30. Been running a semi-syn (a thicker one at that...) 10w30 and it runs like a sewing machine. Likes been said before, GM V6's are not hard on oil albeit if they don't have intake gasket problems.
In my NA 3800 Park Avenue, I used Quaker State Defy 10W30 without problems. The 3800 is a no-drama engine when it comes to oil.
Post a pic of the GS. It would interesting to compare it to today's Regal GS model.