"Always" target melee barrack first

[Shadey]

I think people (and creeps too) go for the ranged barracks just because it's closest to you after you destroy the tower and it's bigger than the melee barracks....

[dune]

^ Half a hero kill bounty is hardly "a bit of gold". But they do distract creeps.

They can give as little as 13 gold IIRC, so it all depends really. Generally you don't need to target them, but you can do if there's nothing else worth targetting.

Ancients of Wind(?) in Dota have higher regen rates which corresponds to the ranged barracks having higher regen. I think shrines are supposed to replace ziggs/moon wells which don't really do anything in Dota except distract creep fire and they posses no regen.

In DotA, AFAIK, they are equal armour and hp regen now, but yes the shrines are just the random buildings scattered in the bases.

[LightRain]

^ Half a hero kill bounty is hardly "a bit of gold". But they do distract creeps.

Agreeing with OP 100%, FF the melee rax for the advantage in pushing down the lane.

i) at the point in the game where you are breaking shrines so your creeps hit the enemy tree faster, it really doesn't matter anymore
ii) Melee rax has better payoff but sometimes you can guarantee a ranged rax kill (due to creeps going to that one first) where you couldn't guarantee a melee rax kill. It's not completely mindless.

[Etdashou]

For the shrines, I think it can be useful to kill them, as it makes your creep faster to attack the main big building. Also it gives gold if you last hit. I think I saw once like 134 gold... but some tests on EM or notEM would be nice to be sure.

However it is not as important as a rax...