Paula's son wants a PC to play Minecraft on for Christmas. Leo says that for Minecraft, any PC will do because it's not very demanding. As her child's tastes in games matures, though, he may require a more powerful computer that can handle the graphics. There's a lot of choices for her budget of $600. Leo likes Acer for entry level computers. For gaming, PCs are generally better and she'll likely want a desktop over a laptop. Asus and Dell are good options as well. Avoid going to a "big box" store because they usually are selling older models.
Dell has a gaming brand called Alienware, and its laptops can handle the graphics. They aren't entry level rigs, though, but Dell is a great place to start. An i5 processor with Iris or Iris Pro graphics. It should have at least 4GB of RAM, but 8 GB would be better, and a 14 to 15" screen. Dell's Inspiron is a low end laptop with pretty good performance for that price point. The Chatroom says that the X51 Desktop from AlienWare is affordable.