What specific dangers do we fear in reading the classics? Falling prey to false ideas, pride, and an over-reliance on the intellect come to mind. There is also the possibility of reading things that might tempt us to other sins, like lust.
I've been re-reading the Narnia books, and I came across an exchange that neatly sums up our primary defense. In Prince Caspian, Lucy and Susan, with Aslan, have just been part of an innocent but wild revel of pagan mythological characters. After they realize what they have been seeing, Susan says,
"I wouldn't have felt safe with Bacchus and all his wild girls if we'd met them without Aslan."
"I should think not," said Lucy.
Our main defense against all sin is always the presence and grace of God through Christ; the paths out he provides for these temptations are the same as for all the others: His Word, prayer, accountability to others. If anything starts to come between us and God, then it's time to back off for the present and draw closer to God.
There is also a time and a place for everything. Probably the worst possible time and place for encountering the wide world of ideas is as a young single person away at college. At that age, one has no deep responsibilities to any other human being. One is, simultaneously, tasting the fun of physical independence. The allure of taking on intellectual independence is unbearably strong, when combined with the lack of any sense that anyone else might be hurt by one's new ideas. Any idea that one's parents did not believe in is invested with glamor. You want to believe new things just because you can.
So, just as I plan to teach my children that they are not the center of the universe before they turn two, and instruct them on how to combat lust before they reach puberty, I hope to give them the tools to analyze and question new ideas before they come to the age when the new ideas are so tempting. I'm sure I can't prevent them entirely from stumbling in that area, any more than I can in the others, but I think I can make the right path easier.
A six-year-old will swallow nearly anything they're told; I would be very careful about what I gave them (but of course there are great ancient tales suitable for them). An eighteen-year-old will swallow almost anything that butters up his ego. I think the best age to begin a serious study of classics true and false is about twelve. That age is naturally skeptical and eager to question everything. If properly raised, they're still willing to listen to mom and dad's thoughts and learn together. Then when they reach independence and encounter the ideas in new and different guises, they have that preparation well under their belt.
I would make sure as they encounter new ideas, they also consider the lives of the people who propounded them and the effects those ideas had. Nice as something may sound, how did it work when real people tried to live that way? Intellectual study is also best balanced with physical labor and service to others, to keep one humble and help one see the other sides of life.
Different children call for different educations. A child who is gifted with their hands and not particularly analytical probably needs no more than a second-hand introduction to refuting the false ideas current in the culture: secular humanism, materialism, relativism; plus an exposure to as many literary classics as is enjoyable for them. A child with technical abilities headed for more professional work needs a more detailed preparation; even if they get certification without spending much time in college they will work with people who did. A child gifted to work in the realm of ideas will need much practice encountering ideas, analyzing them, finding truth, spitting out error, and explaining the difference. A child like that will be more susceptible to temptations to intellectualism, but they will also have greater powers of discernment. All strengths come with weaknesses.
For the most part, I am not enamored with the idea of going away to college as a standard rite of passage. Human beings are very influenced by their physical surroundings. When those change, we are more apt to doubt the things we associate with those surroundings. Getting a higher education closer to home helps one keep an anchor in the real world, and remember that one's beliefs will influence others. (Getting married and having children has much the same effect--you start thinking through the consequences very carefully when you realize someone else is going to be following you.)
The main thing, though, is to always keep in mind why we are doing this. Never read a book just to be a well-educated person, to finish a list, to outdo your peers, or to exhibit that you are able to "handle" more dangerous things than someone else. Only read a book if you can do it with the goal of becoming a more godly person, better able to minister to those around you, better prepared for the calling God has for you.