So, many companions in Fallout 4 cannot equip some types of Armour. You can never put human armour on Dogmeat (though some clothing items can be used), Strong will only wear Mutant Armour, and so far I believe Nick can't wear any additional armour.

But does the game give companions any specific boost for equipping certain types of favoured armour to them?

To use Skyrim as an example (as Fallout 4 almost certainly sharing common code in this area) every companion you had with you tended to get boost for wearing Light Armour, Heavy Armour or Clothing.

Is there a similar set up here?

And does anybody know of a list of what type of armour each companion in FO4 is going to best suit them?

You are forgeting one important thing about Skyrim here and that is armor perks which are non existant here(apart from PA ones which i wud assume no companion has except mybe Danse-the core duration one is irelevant for them anyway since they dont use the charge)

So any companion with equipable armor will benfit the most by giving em best possibile armor(defences wise) also you might also want to consider things like your playstayle for example if you are heaviliy orinted into sneaking type of play you might wana quip your companions acordingly, if you want them to melle than PA makes a great choice for any companion etc...

This was largely the conclusion I was coming to, myself.

I guess without running each companion through a toolkit your never going to know if they have perks attached to them.

Obviously Nick won't wear anything other than his Trenchcoat (which makes sense based on discussions you have with him, and it's not like he takes radiation damage) and Strong can only wear Mutant armour because of his size.

But does it make sense to stack other characters in different kinds of armour? Not just as a playstyle choice, but as logical to their character?

Power Armour goes with everything.

My point was there is no armor related perks in Fallout 4 so they cant have any(except in regard to PA which has 2 of them is non relevant for companions, and the other is streinght 10 one so i doubt any companion has it-lore wise only one that wud make even half sence having it wud be Danse if we disregard S.P.E.C.I.A.L requirments), define logical to their character i mean after they travel with you for a while they keep getting into dangerous situations so i wud assume its very logical to quip them with better armor since they cant do it themselves:)