I duno where to start, but this scenario is the only type of game I played after I got bored with standard games. Let's share some experience and game play tips with several civs that we can choose from shall we?
Oh, I play this scenario on noble most of the time.
Another note:
I skipped Mali & aztec...cause they really are ...uh...not up to par IMO.
A.Asian Civs
Japan
It's a decent start, basically you have no enemies at the start. Your only enemy is yourself. I usually load up all the samurais off the island and immediately take over the barbarian town nearby. Having done that. I usually settled one town on the northern tip of Japan.
Then I moved most of my samurais to the west to capitalize on the Mongolian vs China war. Mongols always seem to lose here....their AI is terrible >.< The trick here is to choose when to strike.
1.Easiest method Strike North
Attack the Mongolian capital city. They're practically sitting ducks when the Keshiks charge south. You get probably 2 towns in a decent spot. This will also prevent you from getting into early border tensions with China and still get relations boost from the War Aid you gave them.
2.Slightly harder Strike South
This is really tough but very satisfying to pull off. The culture density is sooo thick in there, but if you succeed, that means a holy city or two for you. Good way to make money and secure an empire. I usually raze a city or two, China is really too crowded to develop properly. And ofcourse I go for coastal towns first to prevent my towns from being culture-crushed.
The Samurais will easily take care of almost all encounter. Just make sure you deny the Chinese of Horses to keep things even.
By the time you're done with the Chinese & Mongolian empire, you probably will roll over Asoka's empire easily (he's badly jungled up) then you can plan to take over the world 
China
This isn't too hard, the Kahn's AI is too dumb to pose a challenge as long you keep a few STR 6 in garrison you can basically focus on hunting those Keshiks down with a few pikemen. It won't be long till he sues for peace because all he can do is pillage / commit suicide on your garrisoned towns. Most of the damage done is temporary, even if he captures a city it will be culturally starved.
Once the Mongolian threat is countered I recommend finishing off the pesky Japanese before they grow more powerful and expand all over S.East Asia. India, should be left for last. Let Asoka clear the damned jungles for you while you mass the necessary force to kill him, (Just don't send in Knights, his Elephants will stop those)
Mongols
This isn't as easy as it sounds in history books. Damn those Defensive bonuses. I basically pillaged every single tile I could while picking towns with less than 3 defenders exclusively while my capital city build up Catapults.
First step, assemble 3-4 Keshiks to the barbarian settlement to the east. Capture it, while the rest of your forces pillage. Cut every road and then proceed to target towns with less than 3 defenders. Make sure it's a coast town,else you will end up culturally starved. >.< After heavy bloodshed in both sides...you probably will stabilize enough and able to take on India & Japan.
India
Crap. Really tough start. Probably Asia's Russia. You start in the middle of jungle, although you have holy city you still face threat from Saladin's forces. No source of Horses and oil either. You have to quickly develop your land to keep up. >_< A Really passive start. You cannot attack anything at all with Elephants. Probably try for Australia expansion for some much needed resources. I'm still not sure how to acquire Oil in the future but at least you got iron.
B. Saladin's Empire
Very. Very. Strong. His empire looks like it's about to fall apart from the thinly spread forces, but I just prioritize Jerusalem and several core cities. Once that's done. You practically will have zero income problems. Definitely go 0% research and focus on upgrading archers to longbowmen for security first.
Garrison slowly then begin a worker force to build your infrastructure. For fun's sake let's not declare peace with the Christians, because once they do, it's a piece of cake. Really, Saladin can't lose as long as he has Jerusalem. For added fun, crush the Malinese, a very non-factor civ with some Camel Archers when you have the time. Whole Africa should be yours.
C. European Civs
I'm grouping them into same category except for Russia. They're so similiar in every way. Well, maybe except for Britain.
British: I find it difficult to break anywhere with a lousy navy and very very dense competition for tiles in homeland (japs have it easier). So I focused on developing core cities after grabbing nearby barbarian towns. Basically I'm ignoring Saladin and went for the Vikings. It's not bad really, but the hard part comes when border tensions just kept spoiling relations and your allies kept asking for tech.
Spain France & Roman Empire : Same problem as Britain, they basically got choked badly and had to maintain a strong enough culture to prevent themselves from being tile-starved by their own allies. And you can't really expand into Russian borders with Settlers, the damn Byzantines won't let you! Only way is to focus on military and strike at them hard while ignoring Saladin completely. (At least you can negotiate with that dog, Vikings & Byzs can't be talked to, damn terrorists)
Russians
They're suffering bad. Reallly bad. At the start of turn I would suggest relocating the settler right next to the iron and keep a stranglehold on the other town. Abandon your capital asap, build workers, clear cut all the forest around it to quicken your build up. It WILL be lost anyway. Set Science to zero and focus on upgrading archers to longbowmen. Oh, for sheer idiocy, just before the Byzantines come in and take your town, gift the city to one of your european allies or maybe Saladin for peace LOL.
Your come back will come later when you unlock Cossacks. By then you'd probably be more interested in expanding Eastwards. I did that, and crushed what remains of Genghis Kahn puny conquest. Ofcourse sporadic strikes against Vikings & Byzantines are encouraged, but I tend to find their town being culture-starved after I captured it....not profitable to keep, end up losign a lot of pop and still have to build culture generators to eke out a living.
Oh, I play this scenario on noble most of the time.
Another note:
I skipped Mali & aztec...cause they really are ...uh...not up to par IMO.

A.Asian Civs
Japan
It's a decent start, basically you have no enemies at the start. Your only enemy is yourself. I usually load up all the samurais off the island and immediately take over the barbarian town nearby. Having done that. I usually settled one town on the northern tip of Japan.
Then I moved most of my samurais to the west to capitalize on the Mongolian vs China war. Mongols always seem to lose here....their AI is terrible >.< The trick here is to choose when to strike.
1.Easiest method Strike North
Attack the Mongolian capital city. They're practically sitting ducks when the Keshiks charge south. You get probably 2 towns in a decent spot. This will also prevent you from getting into early border tensions with China and still get relations boost from the War Aid you gave them.
2.Slightly harder Strike South
This is really tough but very satisfying to pull off. The culture density is sooo thick in there, but if you succeed, that means a holy city or two for you. Good way to make money and secure an empire. I usually raze a city or two, China is really too crowded to develop properly. And ofcourse I go for coastal towns first to prevent my towns from being culture-crushed.
The Samurais will easily take care of almost all encounter. Just make sure you deny the Chinese of Horses to keep things even.


China
This isn't too hard, the Kahn's AI is too dumb to pose a challenge as long you keep a few STR 6 in garrison you can basically focus on hunting those Keshiks down with a few pikemen. It won't be long till he sues for peace because all he can do is pillage / commit suicide on your garrisoned towns. Most of the damage done is temporary, even if he captures a city it will be culturally starved.
Once the Mongolian threat is countered I recommend finishing off the pesky Japanese before they grow more powerful and expand all over S.East Asia. India, should be left for last. Let Asoka clear the damned jungles for you while you mass the necessary force to kill him, (Just don't send in Knights, his Elephants will stop those)
Mongols
This isn't as easy as it sounds in history books. Damn those Defensive bonuses. I basically pillaged every single tile I could while picking towns with less than 3 defenders exclusively while my capital city build up Catapults.
First step, assemble 3-4 Keshiks to the barbarian settlement to the east. Capture it, while the rest of your forces pillage. Cut every road and then proceed to target towns with less than 3 defenders. Make sure it's a coast town,else you will end up culturally starved. >.< After heavy bloodshed in both sides...you probably will stabilize enough and able to take on India & Japan.
India
Crap. Really tough start. Probably Asia's Russia. You start in the middle of jungle, although you have holy city you still face threat from Saladin's forces. No source of Horses and oil either. You have to quickly develop your land to keep up. >_< A Really passive start. You cannot attack anything at all with Elephants. Probably try for Australia expansion for some much needed resources. I'm still not sure how to acquire Oil in the future but at least you got iron.
B. Saladin's Empire
Very. Very. Strong. His empire looks like it's about to fall apart from the thinly spread forces, but I just prioritize Jerusalem and several core cities. Once that's done. You practically will have zero income problems. Definitely go 0% research and focus on upgrading archers to longbowmen for security first.
Garrison slowly then begin a worker force to build your infrastructure. For fun's sake let's not declare peace with the Christians, because once they do, it's a piece of cake. Really, Saladin can't lose as long as he has Jerusalem. For added fun, crush the Malinese, a very non-factor civ with some Camel Archers when you have the time. Whole Africa should be yours.
C. European Civs
I'm grouping them into same category except for Russia. They're so similiar in every way. Well, maybe except for Britain.
British: I find it difficult to break anywhere with a lousy navy and very very dense competition for tiles in homeland (japs have it easier). So I focused on developing core cities after grabbing nearby barbarian towns. Basically I'm ignoring Saladin and went for the Vikings. It's not bad really, but the hard part comes when border tensions just kept spoiling relations and your allies kept asking for tech.
Spain France & Roman Empire : Same problem as Britain, they basically got choked badly and had to maintain a strong enough culture to prevent themselves from being tile-starved by their own allies. And you can't really expand into Russian borders with Settlers, the damn Byzantines won't let you! Only way is to focus on military and strike at them hard while ignoring Saladin completely. (At least you can negotiate with that dog, Vikings & Byzs can't be talked to, damn terrorists)
Russians
They're suffering bad. Reallly bad. At the start of turn I would suggest relocating the settler right next to the iron and keep a stranglehold on the other town. Abandon your capital asap, build workers, clear cut all the forest around it to quicken your build up. It WILL be lost anyway. Set Science to zero and focus on upgrading archers to longbowmen. Oh, for sheer idiocy, just before the Byzantines come in and take your town, gift the city to one of your european allies or maybe Saladin for peace LOL.
Your come back will come later when you unlock Cossacks. By then you'd probably be more interested in expanding Eastwards. I did that, and crushed what remains of Genghis Kahn puny conquest. Ofcourse sporadic strikes against Vikings & Byzantines are encouraged, but I tend to find their town being culture-starved after I captured it....not profitable to keep, end up losign a lot of pop and still have to build culture generators to eke out a living.