Even though the AWs mentioned have a similar effect, it is nearly impossible to directly compare them. Too many influencing factors.
If you are serious about tourney play from day 1 of your elvenar career, you will have Needles at lvl 30 (and the Shrooms as high as necessary) long before you reach the Simia. So the question is more FA or Simia, since yes, you definitely want to make the switchover from barracks to Merc camp somewhere around there as well. But really you want to upgrade them both as often as you can
Then again you have the FA available rather early on as well and can get a headstart on that one long before the simia comes into play.
The training grounds + VicSprings is in my eyes a waste of space and KP, much better put to use in maxing the others. Maybe once you are past 500 AW levels you could do that for the sake of completeness or something...
One AW you have completely forgotten is the MM: The hitpoints you get make your troops survive, which is also a way of getting free/more troops (and as the Simia does, gives you the troops for free, not having to pay supplies for them again). But also this AW should be somewhere above 20 early on.
Well and then there are all the "free troops" AWs (and event buildings), but the AWs I would not consider (unless you get them for a different reason, like Shrooms) The troops are not actually free: They cost space (for the building) and KP (for upgrading instead of more important AWs)
Ah now that we have started: Damage increase is also a way of making your troops survive better, meaning more free troops... but I think I better cut off here...