Use very little throttle with the GTO and bring the clutch up smoothly and progressively. Heck, if you bring the clutch up slow enough in first gear on a flat or down sloped surface, it will start up without any throttle.
Basically you won't want to rev the engine too much while you're slipping the clutch (i.e. bringing the clutch up from the floor). During this time, the clutch is not fully engaged and is slipping against the flywheel(?). More power (especially from the GTO) causes the two to slip more than they should and it causes premature wear on the clutch.
Burning up the clutch a little bit here and there won't cause permanent damage generally. But your goal in driving should be to slip the clutch as little as possible while maintaining smooth takeoff & shifts. At first you will want to be slower with the clutch to get used to it, over time you will get to start up very quickly in 1st with the GTO.
Don't feel too bad if you smoke it a few times. One time not long after I got a Stick 101 lesson from a friend, I pulled up to a stop light on an exit ramp, which was at a VERY steep incline. Of course some ass honkey decided to pull VERY close to the back of my brand new $30K 2006 GTO. I was a bit nervous.
I had been starting off in 2nd gear to get used to the clutch and was so nervous, I forgot I was still in 2nd. Trying to get the clutch in ASAP and take off so I didn't roll into the dbag, I revved like hell and had the clutch maybe half in. It moved just fine, but dear GOD did it stink of crispy clutch. It still smelled 10 minutes down the road when I parked at wal-mart. And luckily there were no permanent effects once the clutch cooled down
How many miles on the 04 GTO? After a while, the stock clutch on those heavy cars can wear a bit and it will slip easier than a brand new clutch. If you ever have to replace it, get an LS7 clutch and flywheel. Same price as the stock one, fits fine and will hold about 500 RWHP with stock driveability.