Xerxes the Achaemenid is better than Xerxes King of Kings for playing Achaemenid Persia and I'm tired of pretending he's not. The extra gold boost from Unique Improvements makes it so you can field a large army of cavalry in the antiquity age, ignoring the maintenance cost hurdle most leader/civ combos have. Grab yourself an appropriate city state or two for the unique improvement yields you desire, and watch the gold and culture stack up over the age as you grow and place more of them alternating with Pairidaezas. The overflow of gold will allow you to field more cities and urban centers than King of Kings could hope to.
War? That's not a problem when you can buy in expensive cavalry as soon as you grab The Wheel. Be sure to build Terracotta Army early because you'll most likely be getting a free commander from a narrative event. This will bring your total of commanders up to 3 without ever hard building one. Most of the AI will only have 1 or 2 tops and they don't know how to use them anyway. You can have 12 units packed in these bad boys and a company of cavalry riding with them. You'll likely have warriors left over from early barb skirmishes to upgrade into immortals and fill up space. Immortals are a weaker unique unit, but they're bodies to fill up spaces and deny enemy movement and with the Persian traditions they'll be beefier and dirt cheap to maintain.
Culture won't ever be an issue. You'll be able to snipe the wonders you want rather easily when you have every unique improvement generating culture. Heian Japan will outshine you, but that goes for most civs in most situations.
What about science? I'm playing a deity game right now where I ignored the scientific city state and opted for the economic one and the militaristic one. I grabbed Emporiums and the settlement cap. I didn't build a library until I already had Dur-Sharrukin built to deny it to my opponents and defend my capital from the AI that surrounded me on 3 flanks on a tight pangaea. Due to conquest of two capitals I'm in second place for science near the end of antiquity. My hordes of cavalry and 3 commanders allowed me to fight a defensive war against Blackbeard and an offensive one against Ashoka World Conqueror at the same time with ease, all while gaining valuable commander levels. I rushed Tier 3 units instead of Academies as well. Grab the Step Pyramids for most playthroughs to balance out your yields, as long as you have enough tiles to place them, but if you're good at war you don't need them.
I have Xerxes level 10 and this is my first time trying Achaemenid. I'm never touching King of Kings again, unless it's to Assyrian my way to 20 future techs without causing towns to go negative yields.