The order would be
1) The Friendly Game
2) The Porcupine Game
3) The Driving Game
4) The Yo-Yo Game
5) The Circle Game
6) The Squeeze Game
7) The Sideways game
I'm pretty sure that is the order, I'm doing this all from memory.
Technically there are 4 main games....Friendly, Porcupine, and Driving. The other 4 are just mixing the first three.
Gingerrr...to be honest you don't need anything to play the games. It is recommended that you use a carrot stick simply as an extention to your arm, but it's not 100% needed (though I do find it alot easier). Also what I find makes it easier but not really needed is a longer lead rope. I have a 12 foot lead rope and I want to get the 22 foot because I think the 12 is too short lol
Here is a good explinatino of the 7 Games on how to perform them http://www.wikihow.com/Do-the-7-Games-of-Parelli
The only one that I don't agree with 100% is their one on The Friendly Game. Just being with your horse, sitting next to them, grooming, talking to them, etc....is The Friendly Game. It can be on the lead or off of it.