Hmmm… this is an interesting question. If you want to do individual stocks, I think you should do it more as a “get them interested in investing” vs. “put some real money aside for their future” kind of thing. Why? Because a small number of individual shares of stock is a real pain to deal with, and is an investment strategy with very volatile returns.
Most public companies of decent size have a “direct investment” program, and you can often even request actual physical stock certificates, which you are never going to get from a broker. (Some companies have really neat-looking ones.) I could see a kid excited about a couple shares of a toy company or Disney or something. (I’d go with a company that doesn’t have very expensive shares, so if the investment gets lost or forgotten about, no real loss occurs.)
If you want to invest in their future, an investment in a Total-Stock-Market Index Fund are probably the best, but I don’t think they’ll be super excited about getting a plain envelop from The Vanguard Group four times a year.