Wow!!! This is going to be fun! Shaking my head in amazement at the careful construction of combined troop possibilities here. I seldom build combined unit stacks. But in this game I expect I'll be wanting to do a great deal of that.
Here are my scattered pregame thoughts. These are highly subject to change as the map unfolds, and as I play the game and find out I was wrong
I'll go slow in this game. It looks way too good to race through, I'd rather play it slowly and savor it.
Based on what's visible so far I will irrigate the start tile and move the settler NE. But before doing this I'll move the scout, just in case he sees something better. I'll start the scout with a step SE. Where he goes next I'm not sure. What he sees may affect the decision. If nothing special is visible at this point I might make his second step to the west. That would reveal a few more tiles which could change the settler's first move, though that is unlikely - only one of those tiles is grassland which could have cattle.
Depending on surrounding terrain I expect to end up with one or two settler/worker factories using the lovely wines.
I'll avoid early warfare if possible. One exception will be if war is necessary to claim iron and horses. Another possible exception would be if a neighbor builds Great Library. Aside from those possibilities I'd prefer to spend Ancient Times building up for the massive wars which will come in the Middle Ages.
I haven't decided yet but I'm considering going to Monarchy and staying there in this game instead of my usual choice of Republic. Once we hit the early Middle Ages this game is likely to be continous war till the end. Monarchy without war weariness, or Republic with more income? I'm not sure. After exploring the map I'll decide. Luxury availability and the likelihood of being at war with multiple Civs simultaneously later on will affect my thinking on this.
The four unique units present many interesting possibilities. They'll all mix nicely into hordes (stacks

) since they're all fast.
As others have said, Turghaut Cavalry will be good defenders. I think I'll want at least two of them in each Mongol horde. Having two or more in a horde will allow the horde to continue if one is wounded or killed, and will allow temporary splits of the horde into two or more sub-hordes. These units are far from invincible defenders though. They'll be facing strength 4 attackers. I think it will be important to also use the horde's fast movement to take advantage of defensive terrain.
The other three units are attackers. Each has a different advantage. They all share one weakness: low hand to hand attack strength. They're weaker than Knights in this regard. It will be important to utilize their archery. When attacking cities this may mean that we need large numbers of them. If, as I suspect, archery works like bombardment against cities, then many shots will be "wasted" reducing the population and improvements instead of hitting defenders.
The Ordu Archer seems the weakest attacker, especially with hand to hand attack strength of just 2. But it can fire twice per turn at strength 4. This will be an advantage in some situations over the Khorchin which can fire once per turn at strength 6. And it can eventually upgrade to Cavalry - a major advantage if the game continues to the Military Tradition stage
The Khorchin is in the middle of the three attack units I think. It has an ok hand to hand attack strength of 3, a single shot per turn at 6, and that single shot can kill a redlined enemy. In general it seems best to use these units to take advantage of their powerful archery instead of attacking hand to hand.
The Bagatur Horde seems the most powerful special unit to me. It has the same stats as the Khorchin except that its shots cannot kill a redlined enemy, it has defense 2 instead of 1, and it has the blitz capability. The blitz capability will be this unit's advantage. In seiges they can use three strength 6 shots. If these units are used to dispatch redlined enemies in hand to hand combat, they'll get an instant upgrade to elite by winning twice in one turn, and thereafter they'll have plentiful opportunities to produce leaders. This unit should fare well on its own in some situations. Its defense of 2 is barely acceptable for a loner (an accompanying Turghaut Cavalry would be better of course); in offense it can be very powerful, taking two shots at an isolated enemy unit and then engaging it in hand to hand combat all in the same turn. I think this unit may have been underestimated so far. Which is better: 3 Khorchin at a cost of 60 shields (3 archers) + 90g (if we have Leonardo's, 180g if we don't), or one Bagatur Horde at a cost of 60 shields? If the Bagatur Horde does indeed get to take three shots per turn, then both of these choices result in 3 strength 6 shots per turn. But the Khorchin can be prebuilt before we learn its tech. And has lethal shots, and each of the three Khorchin can move and shoot in the same turn. OTOH, the Bagatur Horde has better leader generating potential and costs less. Decisions, decisions ...
It seems to me that the special units become progressively harder to build in the following sequence:
A Turghaut Cavalry can be created by retraining a 10 shield Warrior.
A Khorchin can be created by retraining a 20 shield archer.
An Ordu Archer can be created by retraining a 30 shield Horseman.
A Bagatur Horde can only be created by building one at a cost of 60 shields.
Trying to save gold for the upgrade paths will clearly be important. Whether that is possible, and how to do it, will depend on how the map unfolds.
It may be useful in this game to leave one or more productive towns unconnected to the rest by road. Those towns would be able to continue producing warriors and archers for a long time, who could then travel to a nearby connected town and be retrained to become Turghaut Cavalry and Khorchins. It might even work to have a separate town connected only to horses, to build Horsemen for upgrading to Ordu Archers. This seems a dubious possibility though - hard to set up and only 20 shields are saved on that upgrade path.
My initial thinking is that ideally I'd want my hordes to consist of Turghaut Cavalry, Khorchins, and Bagatur Hordes in a ratio of about 1 : 3 : 8. The Turghaut Cavalry would act as defenders. The Bagatur Hordes would wear down enemies with their archery. When the enemy is down to redlined units, the Khorchins would fire on strong defenders, the Bagatur Hordes would take out the weaker ones hand to hand. But I doubt I'll have any chance to actually build hordes with that dream mix - it is a very expensive mix to build. And has no longer term potential to upgrade to Cavalry. In practice I'll probably have hordes with some Turghaut Cavalry, many Ordu Archers, some Khorchin, and some Bagatur Hordes. And I might have some isolated Bagatur Horde units wandering about.
Research: I'll start with research at zero. Our starting techs enable building granaries and archers, but they don't enable direct research of any second level tech. I'll try to meet neighbors and find goody huts before starting research.
A bit further along, trying to build Great Library will be tempting. It would enable saving up a lot of money for upgrades to the special units. Nonetheless I probably won't try for it. Limited expansion and a high production town might change my mind. But the downsides of building it are significant too: many shields invested, and slower research. The Great Library approach encourages waiting for the AIs to discover techs. I'll prefer to get ahead them (if that proves possible.)
On entering the Middle Ages the choices become confusing. Feudalism first because it is necessary for all of our UUs? Or Monotheism and/or Engineering first, counting on the AIs to research Feudalism and trade? I'll go the second route if the AIs are researching quickly enough by that time. If there's a scientific Civ in the world that will change things, it will depend on their free tech. But I'll hazard a guess that there's no scientific Civ
Feudalism will give us our first special unit, the defender. I won't want to go on the offensive with just this unit. But depending on the world situation it might pay off to start a defensive war at this date. The first defensive win will trigger our Golden Age (or will it? Cracker, could you please tell us?) and this might be a good time to start one, enabling faster research to the other special units.
After that, which will be better: Monotheism and Chivalry, or Engineering and Invention? The first gives us Ordu Archers and Bagatur Hordes. The second gives us Khorchin and a shot at building Leonardo's. I think I'll go for Chivalry first because I want to start building some Bagatur Hordes early on. And if our Golden Age can only be triggered by Ordu Archers then I very much want to research that path first.
After learning Chivalry and Invention it may or may not be worthwhile to research further. If it seems that domination can be reached with just the special units then perhaps no more research. OTOH, Cavalry are a much more powerful hand to hand unit. Learning Military Tradition, and then replacing all Ordu Archers with Cavalry but continuing to travel with the other units would be a powerful combination! And of course if Astronomy or Navigation is necessary to reach Domination then that will call for further research.
One last thought: It may be possible to trigger a Golden Age via wonders before triggering it via our special units. Either Colossus or Great Lighthouse will satisfy the expansionist requirement. Any of Great Wall, Sun Tzu's, or Leonardo's Workshop will satisfy the militaristic requirement.