Wich lane would you push?

Hi guys,
I wanted to ask you what would you do in this situation.
You already got all their T2 and all your lanes are pushed, you only need to go HG.
Wich T3 is the easiest to push first? And say that you've already taken 1 T3 and barracks, what lane do you push next? (ex. you just destroyed top racks, where do you go?)

T3s are pretty much all the same, though generally midlane is pushed first because it is shorter(easier to counter-push if you won a fight at your T3) and because it is regarded as the "main" lane. Better push the lane that you are closest to, as I said, highground tower zones are no different.

When you take rax you go for the closest available set of rax or straight for T4s.

Midlane is the best lane to push fast due the short range as Dimony said.
But if youre besieging the enemy, id say go for the safe lane cause of the nearby jungle.
If you have top or bot already from another HG, go for the other one to make them harder to defend. If you have midlane, it doesnt matter much which lane to go next.

I heard that it Does matter because of the thickness of the escape pattern that you have to take if something goes wrong.
Say you lose the fight and you have to retreat, it'll be easier to escape from their offlane than from their saflane, and the easiest of all is mid because you can spread in 3 directions if they're chasing

Depends on the line-ups as well. Not just where you fight.

Mid-lane, usually. You have more escape routes and more space to spread out if you are backfooting.

It's really dependent on situational stuff like line-ups, and the lead ups to a tier 3 push.

I don't think they are all as equivilant to push as the other, because the environment around each is massively different. Technically side lanes are a little safer to push because there's less avenues for smokes out of base (But they are harder to push because bigger distance, thus more waves to go through). I think the radiant offlane is safer to push than the dire offlane, because the dire offlane has that group of tree's and the much more enclosed box of death, plus the wrap around with smoke is much easier.

Again I think dire safe-lane might be a little more dangerous to push because again it's much easier to wrap around since you can sneak up and around and get behind the box of death really easily, whereas the radiant safe lane you can only get to the side of the low ground with the smoke.

^This is probably wrong, since I don't play high enough level dota for it to really come up, but the different landscapes of the three lanes must surely make some difference to it.

If you've taken top racks and only have time to get one more set, you should go for bot rather than mid. It's easier to defend mid + 1 than top and bot because there's a bigger distance.

If it's a yolo all-or-nothing push, then go the lane that's closest to their base, which means whichever lane you've been ratting the most. If the enemy has mega creeps, then it's almost always going to be mid.

I hate going middle because they can take you form all sides, better to have the jungle to retreat into, so safe lane.