Hello there! I'm a Super Samsh Bros. Brawl fan too!
Ayway, I am glad to see you and your son wish to dive in to the world of Zelda. it's a great series for anyone wishing for fighting, adventure, puzzling and a few luaghs and tears along the way. considering your son's age, I would recommend The Wind Waker if you wish for a platform game and Phantom Hourglass, Spirit Track, or The Minish Cap for a handheld game.
Now, assuming that you have a Wii, The wind waker is most likely the better choice. The game has a whimsical feel to it, with a good amount of humor and cartoon-y graphics that will probably appeal to your son. If your son has a Game Biy Advanced or a DS. The three other games I mentioned are also good choices with the similar animation (except for The Minish Cap, which is a 2 Dimentional animation.
now, The only Zelda game that is "mature" is Twilight Princess, which is rated T. The reason why the series would be rated 12+ as a whole iss most likely due to the amount of in-game puzzles and backstory given in each game. In each Zelda game, there is the "overworld", which is the overall setting where sidequests and extras are normally found. A good chunck of the game is played in seperate area within the Overworld called sdungeons. Dungeons have a certain item gained that helps you solve problems within the area as wellas defeat the final boss of the temple. The temples/dungeons can get really confusing at times, especially in games like Ocarina of Time, Twilight Princess and Skyward Sword. Not to say that a 6 year old wouldn't be able to figure temples out, but it is just a forewarning so you are prepared for the time of gameplay usually found in these games.
Another unique thing about the Zelda series is that each game is its own experience- even direct sequels. My first Zleda game was Phantom Hourglass, which directly followed The Wind Waker chronologically. Even so, I got the full experience of playing that game without any knowlegde about Wind Waker's plot. So, chronology definetly does not matter in the Zelda series.
And your son is right, you play as Link in every game, although there are some instances were you play as different characters to solve different puzzles.
In conclusion, I would suggest the Wind waker as your son's first game in the series or the Minish Cap if you have a Game Boy Advanced or a Ds lite with Dual_Pack abilities. The Wind Waker is for the Gamecube, but the Wii can play Gamecube games. If you have any furthur questions, ofr if you would even like a recommendation on a Zelda game yourself, feel free to ask
~TheRationalDove