Cometic makes good gaskets. So does Honda.
Since I'm a total newbie, are there any other gaskets or hardware I should replace at the same time? What do I need to watch out for. I don't want to end up ruining my motor.
You should get a full top end gasket kit and replace them all while you have the engine out and apart, especially the rubber oil seal pucks under the cam towers. Don't forget the cylinder base gasket. Removing the head will most likely break the seal and cause it to leak after reassembly. As far as other hardware, it all depends on how much work you want to do, how much you want to spend, and how well you expect your bike to run.