I would have your son do some research into investing. Buying "just a few stocks" usually isn't a good plan.
Why has he decided he wants the company's he wants? Is it just because they are companies he knows are popular?
Are they at a good value right now? Has he decided they are not overpriced? What is their P/E ratio? What is the debt ratio of the company? What is their free cash flow?
Does he have an asset allocation plan? Will he diversify his selection among small, mid and large-cap stocks? What is his goal? Does he want short term investment that he will then sell? Is this a buy and hold plan?
As for where to open a brokerage, I really like Vanguard, but I I'm a big plan of their low expense index funds. The "buy a popular stock" plan I took in high school didn't work for me. Enron and Lucent both went to zero. (Pfizer and IBM did okay for me.) But mostly, the money disappeared. Enron and Lucent were HUGE at the time I bought them, I made some money, and then the company's went bankrupt.