DotA 2 Barracks, Which is better to focus and why?

Here are the stats and bonuses provided by each barracks:

Melee Barracks:

• 1500 HP
• 5.0 HP/sec regen
• 15 armor
• 100-150 Gold to the last hitter + 275 reliable gold to the entire team that destroys it

When destroyed (boosts opposing creep in that lane by):

• Increases Melee Creep damage by 19 points and growth by +1
• Increases Melee Creep armour by 1 point
• Increases Melee Creep health by 150 points and growth by +9
• Reduces gold by 21 and experience by 37 for your Melee Creeps

Ranged Barracks:

• 1200 HP
• 0 HP/sec regen
• 10 armor
• 100-150 Gold to the last hitter and 225 reliable gold to the entire team

When Destroyed:

• Increases Ranged Creep damage by 20 points and growth by +1
• Increases Ranged Creep armor by 1 point
• Increases Ranged Creep health by 175 points and growth by +8
• Reduces gold by 26 and experience by 16 for your Ranged Creeps.

At face value, since you typically have way more melee than ranged creeps per lane, killing the melee building provides more benefit for future pushes. However, the ranged barracks has 5 less armor and will die faster.

When push comes to shove, often you don't really have a choice in which one to take down if most of your creeps are focused on one building over the other you will want to focus fire to take it down faster before the opposing heroes rush to defend. If you do have a choice, you should take out the melee barracks first to put more pressure on that lane with your creeps.

I've played dota for many years. Rule of thumb : go for the barrack you already have an ally focusing on.

In case no barrack are targeted, go for the melee barrack, because of the amount of melee creeps per wave.

Later on in the game, you'll spawn 2 ranged units per wave, from this point on, the ranged barrack starts making sense, but not before that

If you don't have time (i.e. the enemy team is respawning soon or something) go for the ranged barracks. Otherwise go for the melee one.