Reddit mentions of Young Justice (2011-2013) Vol. 1

Here are Amazon links for the digital editions because the physical copies have been out of print for several years and have gotten really expensive.

Young Justice Vol. 1

Young Justice Vol. 2: Training Day

Young Justice Vol. 3: Creature Features

Young Justice Vol. 4: Invasion

Those are (unfortunately) all of the comics that actually tie-in with the show. There is a Young Justice comic series that ran in he late 90s that is also good, but has nothing to do with the show. If you're itching for more comics in this same vein though, I'd check out that 90s Young Justice comic I mentioned and Geoff Johns's Teen Titans run from the early 2000s as they're both phenomenal.

I'd ask what other media your kids are into. That can be a big factor in what comics you'd be into.

The Comic Book Code is effectively dead these days. Though some companies have their own systems, they're fairly loose, so don't take them to literally.

You might try some of the "Ultimate" Marvel books, like Ultimate Spider-Man in particular. This book is really clean and no graphic violence.

Bone is a good all ages pick, and I truly mean all ages. Though the art style is reminiscent of Charles Shultz "Peanuts", the plot is more in common with Lord of the Rings. For $30 you get 1300 pages.

There's a nice book (single trade paperback) called "I Kill Giants" that you may want to give a read before you recommend (as it includes maybe one instance of strong language. It's about a girl who has imaginary battles with giants which represent a larger problem in her life she's unwilling to confront.

Some of the New 52 is age appropriate and some is not. I'd steer clear of Batman, which seems like an obvious pick. Though it's a fantastic read, it's too violent for you to take to school.

Here are some other good picks which aren't racy and don't have any violence above "saturday morning cartoon" level.

Don't be shy about ordering used copies off of Amazon.com or gohastings.com either.

http://www.amazon.com/JLA-Vol-1-Various-ebook/dp/B008YP1WJG/ref=sr_1_1?ie=UTF8&qid=1414516012&sr=8-1&keywords=jla

http://www.amazon.com/Young-Justice-Vol-Art-Baltazar-ebook/dp/B00BHUKU9I/ref=sr_1_13?ie=UTF8&qid=1414516173&sr=8-13&keywords=young+justice

http://www.amazon.com/Ultimate-Spider-Man-Brian-Michael-Bendis/dp/078510898X/ref=sr_1_2?ie=UTF8&qid=1414516204&sr=8-2&keywords=ultimate+spider-man+vol+1

http://www.amazon.com/Ultimate-Fantastic-Four-Vol-1-ebook/dp/B00AAJR39M/ref=sr_1_1?ie=UTF8&qid=1414516248&sr=8-1&keywords=ultimate+fantastic+four