In general, prefer to rush with horses, they prevent the 3rd, or 4th city of your target from having time whip additional defense and they are just damn cool. Generally, this means having to research HBR - a very risky thing as there is a good chance the enemy will have copper hooked up by then and your horses then need to find a new target, possibly with the same results. But not with Cyrus! He only needs wheel.
He starts with agriculture and hunting (both prereqs for animal husbandry). Your cap mUst have some combination (1-3) of corn, rice, wheat, pigs, sheep, cows, fur, deer, or elephants in the workable area. You do not need any techs to see these resources, so I move the starting settler 1-2 turns (or more turns, on epic/marathon) to insure this.
I research animal husbandry first (to know as soon as possible if I have horses in my cap or need to settle elsewhere for them), mining, bronzeworking, then wheel. Build a barracks while growing to a population of 4 (working as many food and commerce tiles as possible to speed population growth and beaker production for BW). With some micromanagement, you can get BW at the same time as your cap hits 4 pop.
As mentioned previously, Warlords Cyrus is Imperial. What has not been mentioned is that imperial trait = 1/2 price settlers! When your population reaches 4, whip a settler (only 1 round into the build is required!). Send your settler to settle ON horses and begin producing immortals as soon as wheel is researched. Allow the overflow from the settler whip to go into a worker, and then switch back to barracks for a population point or two and whip the worker, or ride the worker out at a 2 population.
Connect your cities with roads (perhaps you were lucky and it was possible via river). If it's possible to connect horses to your cap via river, you do not need to settle on them - you can use the time for building roads to build a stable and net 4 immortals in the same timeframe as settling on horses and building a connecting road.
I use my first great general on 2 immortals. I put the general with my medic unit to produce a medic III (perhaps morale for +1 movement) with my highest xp (pure combat promoted) immortal also in the room an continue combat promotions for him. My second great general, I drop on the high-xp combat promoted immortal alone. This will get him combat 4, leadership (+ xp bonus), and blitz. Do not stack attack with these 2 units! Do, however, use the blitzing unit to get 2 kills in 1 round at every opportunity - he should be combat 6 and morale (3 attacks/turn) in no time. Never attack with this unit under 90% success rate - the first time you go for it at 80% (you wont be able to resist as an inexperienced Cyrus enthralled with a combat 6, 3move, blitzing unit), I bet you die. Even at 99%, don't be surprised when he dies. No worries, you will have more GGs. Ok, I admit it, I occasionally (very rare, 1-3 times total) hold my breath and hit at 70%.
The thing I don't like about Cyrus is that all of this absurd power quickly wanes. Immortals are only 4s... With some luck, however, you will have a couple 150xp units by gunships, with free upgrades all the way.
While your immortals ravage the countryside, remember to also secure copper and a commerce city for classic era warmongering. In the classic era, an army of strength 4 units with bonuses against archery and axes (not all melee) is quickly obselete for use as a sole attack unit. Fortunately, they still work well as support units, to mop up archers and help defend. This early religation to support unit status is probably why they get defensive bonuses.
