They aren't exactly there to make sure she doesn't wreck the world. They don't have the power to do so. Yuki Nagato is an alien; Haruhi wished aliens existed, and as a result, Yuki Nagato. Haruhi wished time travelers existed, and as a result, Mikuru Asahina. She wished for espers, boom. Itsuki Koizumi the esper appears. As a result of this, their various groups also come into existence, which is the root cause of the events involving Ryoko Asakura, the esper squad in general, and the rest of the crazy silliness. All of the main events come into existence purely because Haruhi wants it to happen, e.g superhero maid Asahina with magical powers, the thriller/mystery island retreat, and the widely-disliked (though I love it) Endless Eight arc in season 2.
I recommend watching the movie before you start season 2, it ties up a few loose ends in season 1, and leads into season 2. As well as being fucking awesome and furthering the Kyon x Haruhi pairing.
The reason/purpose Kyon has... well, it's pretty simple. He's the only person who initially tried to talk to Haruhi. Everyone else thought she was a weirdo and ignored her. Hell, he thought she was a weirdo too, but he tried to get past that and make friends with this cute loner girl in his class. This resulted in Haruhi sort of keeping him, and eventually it evolved to a point where she can't be without him, as seen in
Another reason Kyon is where he is, is because the rest of the SOS Brigade use him as a mediator; it's revealed early on that telling Haruhi their true identities will lead to widespread insanity, so Kyon becomes the go-between. The plot of the movie builds on this, as well as throwing out some gamebreaking information should it actually become known to Haruhi.
Favourite character is Yuki. She's adorable and I have a plushie of her on my bed. Though I also like alt. Mikuru. Yuki is just so adorably deadpan and emotionless, which is how I apparently act at times.