I’m interested in this, too.
My guess would be that common dwellings and buildings would have been made with the mud brick techniques used up to today -generally rectangular and with flat roofs. Thing is, I don’t really have any basis for that- it’s pure guesswork and more than a bit of stereotyping on my part! I have no idea what the tradition in the Persian heartland was.
There would have been regional architectural variations within the Achaemenid empire, too, as they conquered a range of societies in a short period. It included everything from the central Asian steppe, to the Nile valley and coastal Asian Greek city states, all with their own building methods and aesthetics.
Like I said, I’m interested to find out more details.