I have all AWs and if I didn't I would still want all military AWs.
I suppose if I really needed to pick a couple to start with
I'd go with Martial Monastery for the across the board health benefit
And the Dragon Abbey to make mages hit harder. Which helps because mages are easily killed so if they can kill the enemy faster then they have a better chance to survive.
( but needles is good and toads and victory springs and )
As for Training Grounds and Merc Camp, this depends partly on your race and chapter. The Merc Camp gives you Blossom Mages, far superior to the elven Sorceress, but comparable to the human Priest. By chapter 15, level 3 Frogs are amazing. The Training Grounds gives you Dogs (useful for taking down mages, but they often get killed soon after), and Orc Strategists (excellent for taking down enemy archers and more mobile than human Mortars). There are more obviously, but these are the key units worth focusing on.
Again I have all three
But if I was choosing between Merc or Training grounds I'd go merc
From the perspective of all units being maxed ( so maybe at chapter 10 there'd be some differences)
Like Risen said, as a general rule Blossoms are the superior mage, and those poison toads rock, but also i have found the Forest Rangers ( or is it wardens?) better mage killers than the dogs
I hardly use light or heavy melee anymore. but for heavy melee the Valorians are good
Something to keep in mind.
As you get military buildings and buff your units with Needles, Dragon Abbey, Toad, Monastery
And then when you add in crafted buffs or if you're lucky, Fire Phoenix
Any time you look at the matchup between your Archer ( or whatever) and it says "about equal" well that judgement is according to your base stats. With all your buffs you actually have the advantage.
Why is this important?
Because if the enemy has 3 archers and two heavy melee you may be tempted to use a mix of mages for the melee and heavy ranged for the archers. and you'd have to try to get rid of his archers before they wipe out your mages
but me in that circumstance? i'm sending all archers and hitting auto. because my archers kill heavy melee and my archers also have an advantage over enemy archers.
i hope you can follow what i'm saying there
but that is just one example of lineups where you can use your supposedly equal units to advantage
look at it this way
if you check the tips each unit is best against two other units: mages against heavy ranged and melee, archers against heavy melee ans mages, etc
but with your units buffed on health and damage you have actually now extended their reach so that your mages are good against heavy ranged, heavy melee AND other mages