So a stage like reach 3 cities. How does a team reach that goal?
One team may expand to 3 cities. Another might build 2 cities and capture an Ai capital using a metal. The point is every task can be done in different ways. So a staged process needs to be prepared for teams doing the unexpected or it may fail if a team acheive a goal before it's stage.
Then comes the question of what a task might be. If it is to be a tech then this clearly has to be something every team would go for. Perhaps currency is such a tech. Of course one team may get Currency in 1000bc if they use Oracle and another maybe 400bc. Even CS could be got by oracle on a strong start.
Does staged SGOTM have to define a teams exact strategy? One of the things we all liked about the last SGOTM was the fact it showed many different interesting strategies. So I think allow teams to put their stamp on a game.
So stage ideas?
Techs - Could work. Requiring certain techs could be used to stop certain bulbings paths.

Cities - Seems logical but be prepared for teams reaching x number of cities before a stage is introduced.
Eliminate 1 AI - Unless you create a hub map or isolate us could be tough stopping the top teams doing this before a stage.
Having techs in later stages would only be useful if you wanted them to reach a certain game victory type or perhaps a certain unit like Navy Seals.
Pop level - Reaching a certain number of pop across your empire. 8 cities at pop 1 = 8. One city at size 8 =8. Now this make early expansion more interesting but harder to control or count.
National buildings - I could see Oxford uni being built before 8 cities. HE might work better but this would force a certain game strategy.
Resource - Grabbing 4? happiness or 4? health resource. (Within the cultural ring) Or a total of both!. Downside is it could define where teams place cities if you just do health.
Wonders - A team could be required to build a certain wonder. Again restricts teams putting a stamp on the game.
Build an academy (edit)
Reach a certain great person (edit)
I liked Adrianj idea for side quests. (How to reward these?) (edit)
Of course one thing you could use to make this work is game rules at the start. Like 'old wall of china' idea. The idea being you could not attack China till you had for instance a gunpowder unit/tech. This would force later game play and stop lots of phants/mace/pikes invading the world. Of course don't box in the player at the start if you do something like this.
Of course the challenge will be to make as many VC open to the player. Of course the old ideas of getting the player to do certain tasks before the game end could still be used.
Such as: A city reaching legendary status before you win? Destroy a certain Ai before the game is won. Building 200 cavalry!

Capturing certain wonders.
You could for instance ban the building of world wonders and require each team to capture certain wonders by the end of the game. These could be gifted to certain Ai at the start. Mid/GLH/Great Wall.
Oh the weeks timing would need to be right. Leave others to comment on that. Also if you chose dates to do something by instead of week. I think weeks is safer.
Overall my main concern is teams reaching stages before they arrive. The restriction of game play creating 10-11 carbon copy games. Of course no stage should be acheived by pure dumb luck.
Anyway lots of thoughts hope some help. Not many new ones really.
Oh in terms of wins you could give a target date and reward teams who beat these dates by largest margin or come closest too. (edit)