The Persian Empire is wealthy and powerful but maintaining control over its key provinces is a task for a master strategist.
Achaemenid Empire has a unique position as the master in a confederation of several large provinces which offers interesting choices and challenges right from the start.
Managing such a large landlocked state is not easy and objectives can provide clues as to where to focus your attention, e.g. access to a port for trading. My initial approach is to produce enough food to ensure self-sufficiency, build economic improvements in cities to get more gold and link mines to the nearest city by road to improve production. Building roads between all of your assets is necessary to ensure that units can travel to any trouble spots quickly.
Diplomacy and bribery with your provinces may keep them in the confederation, but there is every chance they will want to go alone. If the confederation crumbles then it is up to you to defend your territory and to retake any renegade provinces.
One of the benefits of this state is that it often receives free subsidies and troops from the Eastern part of the Empire. The Eastern troops often have the self-sufficiency improvement. This makes them invaluable for independent operations across the whole land mass because they do not suffer from a lack of supply.
The Empire requires attention on many fronts and neglecting any one may ruin your plans. It is definitely an interesting and challenging setting.