I don't think it's a bad idea at all to use a few stocks as a lesson in what the market is and how it works, but I do think you are asking the wrong question -- it's not "which stocks are undervalued and will go up?"; it's "how do I teach my kid about stocks?" The actual stock selected is irrelevant for that question -- you are just using it as a tool so he learns (a) that a "stock" is a piece of an actual company that entitles you to that much of the company's future earnings, (b) that it's a lot of work to try to pick the "right" ones and you will guess wrong anyway, and (c) that you should just buy Vanguard. Here is what I would recommend:
1. Do some research with your kid into companies he may be interested in. Narrow it down to 3-4. He can read the company reports, and you guys can talk about what you think is going to happen, why you think this is a good stock, etc. Then buy a few shares of one of them.
2. Then watch what happens -- he can track the stock, read the news about the company, see whether the promises paid off, etc. No matter what happens, *do not sell.*
3. At the end of a year, sit down again. Look at how his pick did. And look at how the *other* stocks that he liked but didn't buy did, as well as various index funds. Note: make sure to point out the fees that he paid for the privilege of buying the stock (and thus will pay again if/when he chooses to sell), along with the effect of dividends/capital gains.
If he wants to continue, do the same thing again. But he has to do the same research - if he were starting over today, would he still buy the same stock? If so, why? If not, why not? Talk about all of the high-paid MBAs and Ph.Ds out there getting paid to do the same thing he's trying to do (so how does he really think he is going to choose better than them?). If he makes some money, great; if he loses, even better (the worst-case scenario is that he ends up being the monkey who throws the dart and beats the experts for the year).
You're not actually teaching him to pick stocks or to trade -- you're teaching him about what stocks are and how they work; you're teaching him the fundamentals of evaluating a business (i.e., that it's a lot of work, not just throwing money at a cool idea); and perhaps most importantly, you're teaching him how hard it is to predict the future, pick winners, outsmart the hedge funds and quants, etc.
We are doing this with my DD - her bat mitzvah money went 90% into Vanguard, but her grandpa gave her a little that was specifically intended to teach her about stocks and investing and all that. Frankly, she is lazy, so I can't see her really wanting to do the work of stock picking on an ongoing basis. ;-). But I hope she does lose on some of her picks and does worse than the indexes overall, because I'd rather she learn that lesson now, when it is "play" money, than when she is out on her own trying to figure out what to do with her own hard-earned savings.