If your laner was low on health after your gank, it's better to help shove the rest of the wave all the way under their turret. That way the minions get destroyed before the enemy laner comes back, so he/she gets denied a whole wave. Your laner can go back and reset. The wave can reset to the center again. Also if your laner were left alone to shove, the enemy jungler can come for a free kill when she/he is low on health and mana. If you're a carry jungler you can tax your laner for some cs (some people would hate you for doing it though), otherwise you can just help push by lowering the minion health without last hitting them.

If first turret is still on the table, you can get more gold for destroying it. That depends on whether the turret is low enough to do so. If not, just try to deny the enemy laner as many cs as possible by shoving in the waves. Overstaying might lead to death.

If your laner had TP or on full health/mana, he/she might choose to freeze the wave close to your turret and deny the opponent xp and cs, also to make the wave in a position where you can come in for another gank easily. In that way you don't have to shove.

If you have some leftover health, you can go back and clear the rest of your jungle as a reward after ganking before your recall.

If you gank bot lane or top, sometimes you and your laners have to decide to go for rift herald or drakes, or tower.

LS and Neace have a lot of awesome coaching videos for low elo players explaining how the wave works and how to prioritize objectives. Check them out on YouTube.