Is there a specific preferred order of operation of signals?
There is no preferred order of operations in signal analysis.

But you should note that the order of operations performed on a signal matters. You can think of these operations like matrices. Much like a AxB != BxA (generally), performing operation A, then operation B on a signal results in a (usually) different signal.

Take for example:


(Reflection at t = 0, then shift to the left by 1)

vs

 (Shift to the left by 1, then reflection at t = 0)