There has been much discussion of how to play different civs depending on traits, UUs and UBs.

Ignoring a given game’s condition specifics, what is the best time to attack a rival civ? In some threads I have read that as Sitting Bull is a slow techer, you will have an easier time post medevil era. And many agree that Shaka is ASAP as his threat just continues to grow.
Toku is another to wait for. The only games I have seen Toku do well in are those where I was his budo buddy.
Rome is easy - Prats are tough. Hit ‘em before iron is hooked up or wait till maces.
With his super courthouses and Landershnats (or whatever), its best to hit HRE before those courthouses are built. Otherwise Charlie will speed up research or production, making him tough to conquer.
I like to hit Mansa Musa early too, before he gets too far ahead in tech. He often goes for an early religion, delaying his skirmishers, making him an easier target. If I let him go too long and he’s not been in other wars, I find him to be a tough opponent.
In fact all the early religion targeting civs are probably good early targets for the same reason (Can anyone name them?).
What about starting conditions of opponents? If I see a close civ with a heavily forested start are they easier? How about those with bad starting techs, limiting growth and production in those crucial early turns?
What about protective in general? Before longbows? After medevil?
Whudya think?

You kill Musa off?!?!?!? He's great to have in the same if you just keep him at cautious or better. He's always up there in tech so I've always got someone to trade with. I just beeline to my prefered techs, the AI always goes a slightly differant way so we can trade our techs and it doesn't take long until the pair of us are shooting off in the distance from the other civs. He tends to get the +4 fair trading bonus quite quicky as you have to be generous in trades with the AI, which should get him up to pleased.

Tbh my approach tends to be more on when I'm ready to attack, not when I think it'll be a pain to the AI. I'll avoid Rome until later in the game unless theres a good rush opportunity. Protective civs I take more consideration of, but just playing the obvious there, I'll hit them as soon as I get catapults, but before they hit longbows. If they reach the bows, I'd leave it until I get cannon

If I find myself near Cathy I tend to either take her down or at least vassalize her as early as possible. In one game, however, she and Ragnar were neighbors and it was fun bribing them to DoW each other again and again...

Hannibal also seems to have a tendency to build these monster stacks in his cities so I either try to knock him out early or make him my best buddy.

I play with random personalities so the AI are always different.

You kill Musa off?!?!?!?

In my current game, he was right next to me and shrined hindu and confusian holy cities with no metal and I (drawing Napolean) had iron in Paris' BFC.
(I GE-ed the AP after trading for Theo, got a prophet, bulbed Islam & got the SM. Research is at 100%! This may be my highest scoring game ever)

You kill Musa off?!?!?!?

In my current game, he was right next to me and shrined hindu and confusian holy cities with no metal and I (drawing Napolean) had iron in Paris' BFC.
(I GE-ed the AP after trading for Theo, got a prophet, bulbed Islam & got the SM. Research is at 100%! This may be my highest scoring game ever)

Er... it mainly more depends on yourself than on your rival.
personally, I attack when the number of unit is making me bankrupt, and every trash city is bitterly whipped/drafted to POP.1

Because we must finish a war quickly, before some global voting make you stop.
And with enough troop, I don't mind if the victim bribe some . .. .. .. .. . against me.

Rule of thumb: Attack techies early (as they are soft targets) and attack aggressors late (as they tech poorly as the game progresses). Of course, aggressors may decide to attack YOU early, which means you either have to prepare to attack them or, preferably, buddy up to them (which can be hard to do, especially if they are close by). In general, you want techies close at hand (so you can attack them before they run away in tech) and aggressors far away (so they don't attack you and so you can attack them later, once you have a strong tech lead).

An alternative if you get enough land is to just sit there and trade whore to a ridiculous tech lead then stomp all over every single person that wasn't in your trade circle and is 2 eras back.

I go by overall power, a quotient of tech x numbers. If Gandhi has 4 cities garrisoned by infantry and not a lot of production capability, I will probably feel froggy enough to mount an attack with cavs/rifles/cannons in the numbers I typically bring. If it's Monty with the stacks he likes to build, I've got to be sure that no matter what my tech lead is, that my numbers and production capability can mostly keep up.

The best time to attack is... when you are strong ;)
Or as Moltke said it: "The best strategy is always to be very strong"