The sad fact is, Sony is only including the standard composite cable with the system even though it's an HD capable system. That means just the Yellow/Red/White connections, with no HD signal. You can buy the component or HDMI cables seperately. If you want 1080p, you have to buy the HDMI cable. Component will allow 1080p for games, but there is a copy protection scheme that prohibits the full 1080p signal through component cables when watching Blu-Ray movies. So your best bet is to get the HDMI cable.
As for using PS2 specific stuff, I'm assuming that Sony will come out with an adapter via the USB slot, that or a third party will release one for these peripherals. The Guitar Hero II is fairly popular, so I'll do some checking and see if I can find any information on an adapter for this.