@Trapezoid, asking questions is good. It shows that you're thinking. Yes, you may build a construct as soon as you like. If you really wanted to you could make a construct before your first creature, although that's hardly conventional.
Typically, a Construct is a beefed up version of the corresponding creature, although you can make it as whatever you want (with-in reason).

@Jay, that is a very fitting theme and art. I'm yet to find a suitable theme for Calvartem.