The order of integration is not important when the other integration variables do not appear in the limits, so usually you can rearrange the integrals to your liking. If, however, a function of $\theta$ appeared in the $r$-integral's limits, you would be forced to do the $r$ integral first.
I'm not sure why you find it hard to do the $r$ integral first, though. Doing the $\theta$ integral first is like tracing out the whole circle at a fixed radius and then integrating over all radii. Doing the $r$ integral first just traces out a straight line that you then integrate around a full circle.