I always read to my kids from the King James version and just interject lots of explanations and applications. They are allowed to ask questions whenever they are confused and we also have open discussions whenever the topic leads them to another point of realization. Although the big guy is only 5, after about one week the old fashioned language was no longer any more difficult for them than any other book with large words would be. I am amazed at how often they pick up on ideas which I thought were WAY beyond them (sometimes beyond me!) and apply things to life situations.
I think that the Bible (along with a good concordance and cross references) is the best source for studying the Bible because one is able to completely avoid any opinion or additional doctrines which can be added quite innocently by even the most well-meaning pastor and focus simply on what the Lord has to say. We have been moving through the bible as it was compiled (Genesis first, Revelation last) and whatever we read during the day, they explain to Daddy at night so that I'm sure they are really getting it.
One warning with this method is that it includes ALL the stories and everything in between. At first I was a bit concerned when we got to the story of Dinah because of their young ages. My son noticed that I glossed it over a bit more than the others. (Not any skipping, just less explanation of the unknown) and that made him even more curious. Since then I've learned that truth is nothing to hide from children, as long as it comes gently and with reassurance and hope. Just as I would never give them false assurance of winding up in Heaven by luck, but instead let them know they are sinners with hope in Jesus Christ, so will I share every truth I find in the Bible.
Okay, I guess I got carried away, but the point is that I just read them the bible and figure that we will cover all the bases in time while keeping the focus on the Word of God. I probably should have just said that to start with!!

~Layla