I'm looking to build some decks that are roughly balanced with one another to pass around and try to give to some friends. I also want it to be a good deck-building experience for me. I've read some different "theories" or "principals" on the Internet, but I'm wondering if someone can give me advice that's a bit more tailored to the content of the Core Sets and the Expansion boxes.

Secondly, I'm curious which of the six decks involved could be primed for tournament competition the quickest? There's a regional event coming up that I'd love to participate in, and while I expect to get smoked, I'd rather not show up with some stupid deck and get laughed out. Having a fighting chance would be nice.

I would say that the lannister expansion is the strongest if you only have the core set. The lannister expansion includes many good cards, and all of the strategies do not require specific cards outside of the core set and expansion (Targ dragons needs dragon lore, stark kill needs bear island and no quarter, ect.).