Will my first four Squaddies always be one of each class?

This is a known feature in XCOM games with classes. First, the game checks if there's any classes you've never had a soldier of, and if so it picks between them with an even chance. Since it rolls them one by one, your first 4 rookies that survive a mission will be different classes. Second, it compares the numbers of each class in your barracks to make a roll. If there are classes with 0 living soldiers, they will be much more likely than those with 2 living soldiers, and ones with a single soldier alive are more likely than those with 4.

They changed it a little bit in XCOM: Enemy Within. The first step is the same, but the second roll is replaced with a draw from a deck of 16 cards, 4 from each class, with the top 3 cards discarded. This means that if you promote 17 soldiers (including the first 4 from step one), you'll get at least 2 of each, and quite likely 3, but never 6 of one class.

Source: ufopaedia.org