Actually there is a component cable for the GameCube, although you do have to order it from Nintendo...one thing though, if you go that route, you have to use the red and white analog audio connections anyway. The back of the GameCube "says" Digital AV but it is really only Digital Video especially since the cable you get from Nintendo only has the three component connectors ( I know I have one ).
I believe there is a component cable for the PS2...Ken is correct about the digital out for the PS2...
As for component being too expensive (it looks better than composite or s-video, not to mention, your TV has inputs for it
), Radio Shack (yes, I said Radio Shack
) has some good inexpensive component cables as well as Fry's (provided you have one)...Target has some good quality component cables as well...You could look at Best Buy or Circuit City, but stay away from Monster...Expensive for quality available elsewhere...also check Home Depot and Lowe's...they have been carrying component cables too...
It appears that the receiver you have, will pass-through everything via component...centralized switching is a good thing.