If they get a desktop, will they need a monitor as well? If so, you might be able to get by cheaper on total initial cost with a laptop. However, unless they need the mobility of a laptop, I would still go for a desktop. I just have had much more longevity out of desktops than laptops. Not to mention they are easier to repair should something go wrong, and can be upgraded as well if the need arises later.
I recently purchased an HP laptop for my wife with a 2.4ghz i3 for 360.00, because she wanted some degree of mobility. It is decently fast, but for the same price you could get a much faster desktop, sans monitor.