I agree with rexstardust. For someone who's curious about superheroes but is new to the medium, the Ultimate comics are good. The Ultimates may stray too close to the violence thing (and also depends on your opinion of Millar). But Ultimate Spider-Man is one of the most enjoyable superhero comics I've read in years.
There is surprisingly little mainstream superhero comics that one can approach as a newbie. I dare you to hand someone a non-Ultimate X comic, or Spider comic, or Bat comic or Justice League comic and see if they can make heads or tails of it.
Y: The Last Man would be fantastic for a new reader, in my opinion. A great idea at its core, likeable and well developed characters, humour... it's great. Collected in 3 TPS so far.
Fables is another one that's worth a shot.
Hopeless Savages is a black and white Oni book with a lot of heart to it. Centres on the children of a punk rock couple. One of my favourite books in years.
