Help with buying stocks as gift

I want to buy a few shares of stock as a gift. The purpose isn't to make money or anything, more just for bragging rights for the giftee.

Neither of us has a portfolio or anything like that, and I don't know anything about buying stock. Is there any easy way for me to purchase some shares as a gift? (And the company isn't available at those 1share sites). Also note that I'm only purchasing <$100 worth of stock.

I was thinking about making an account under the giftee's name since official certificates aren't available anymore.