Pros and Cons of Pushing lane?

Solution 1:

Is stalling the game still a viable choice ? Should I rush the structures instead ?

To clear up things initially: When you are able to and if you are in no danger of being punished, destroying structures is always the way to go, because

• you gain a significant amount of XP which can be the difference of gaining a talent tier in time or not.
• you deny you enemy a safe retreat point.
• if you destroy the healing fountain, you remove a crucial source of sustain for your enemy during drawn out fights over the objective.
• on maps where the objective directly attacks structures (Sky Temple, Haunted Mines, ...), you get one step closer to victory.

However, this assumes that you can get out safely. While it may be worth to die if you can destroy a keep for it, dying for a few towers or a fort is usually not worth it, unless it is very early in the game where deaths don't matter that much and there no objective coming up before you respawn.
Stalling the game is a viable strategy if you play a composition with lategame heroes (Abathur, Nazeebo, Raynor, ...). Your goal then is to not fall too far behind in the early game to dominate the late game. This does not mean to intentionally leave enemy structures alive when you could destroy them though. It just means to not take unnecessary risks, like rushing structures when you don't know if you going to get out alive.

So, when do I push lanes and when do I not?

First of all, pushing lanes is usually a good thing, since

• your minions provide you with more vision on the map.
• you enemy loses vision on the map.
• it enables you to safely deal damage to enemy structures since the minions tank the tower shots.
• minions alone already deal a respectable amount of damage to structures if not cleared in time.

The principle mentioned above of course still holds: Always make sure you are not overextending is lane and getting picked off. While is may be worth to die for structure kills, it is never worth to die for a minion wave.

So when do I not push?

There are circumstances where pushing a lane actually hurts your team. You should always consider the following things:
A far out pushed lane makes it significantly more difficult to safely soak XP on that lane, since you have to move deeper into enemy territory, where it is far easier to gank you. On Tomb of the Spiderqueen this is very problematic in particular since it denies you an easy way to collect gems.
At the same time it is a lot easier for the enemy to safely soak the XP on that lane. Especially when there are The Lost Vikings or Abathur on the enemy team, you should avoid pushing the lane too far, otherwise they can safely soak the XP while sitting behind the gate.

And how do I not push lanes?

If you have an enemy hero in your lane, then it is basically impossible to push the lane too far (unless you have a very favourable matchup), since they can just clear your minions as well. In that case the best course of action is usually to clear their wave as fast as possible you can help out at another lane before the next minion wave arrives.

If you have no lane opponent and you don't want to push the lane out for the mentioned reasons, just mount up and stay in XP range of the enemy minions (about the sight radius of your hero). This allows you to quickly get out if an enemy gank is coming your way while still providing you with all the XP in the lane.

As a side note any more stacker than those aformentioned ?

With the introduction of quest talents, there are actually a lot of heroes that can sort of be classified as "stackers". Some examples of heroes like this are Raynor, Falstad, Artanis with Seasoned Marksman, Khael'thas with Convection or Azmodan with Taste for Blood. All those heroes gain a huge lategame powerspike when their level one quest is finished.
Heroes with a built-in stacking mechanic are actually just Nazeebo, The Butcher, Diablo and Dehaka.

Solution 2:

The thing with LoL is you wanted the creeps to stay stacked on your side of the lane so you could farm gold and become more powerful without worry, while simultaneously making it harder for the enemy to do the same.

In HotS though, last hitting and gold aren't a thing, you only need to be in the area to receieve xp so this sort of denial doesn't have nearly the same effect. This also goes for shoving the wave into their tower. You aren't denying gold like you would have done in LoL, but it does get chip damage on the structures which is important in itself.

Another important aspect is that there is no junglers in HotS. So it will be more easy to tell if an enemy gank is coming because another hero from the enemy team will have to leave their lane. This is easily observable and can be called out and avoided. However, because of mounts and a smaller map size compared to LoL it will take quicker reactions to prevent it so some faster heroes may still pose gank threats.

There may be some heroes that require a quest completion or certain late game trait to become powerful, or you happen to have unmanageable lane opponents that would make it safer to stay under your towers. If it is your lane opponents then you could always ask another team member to swap with you since lane meta is not very strict compared to LoL.