First, be aware of lane taxing. A jungler can tax lanes, which means take their cs. If you take the kill on the gank, just leave unless the laner pings for help pushing - you took kill gold so don't tax. If the laner got the kill, they're ahead due to that kill gold. So you can tax - anywhere from 4 to 6 minions is a good upper bound. If you don't get a kill on the gank but force a recall or make them use flash for example, you can tax 1-3 minions. The purpose of taxing is that ganking takes time, if you gank and always let the laner take the kill and never tax, you'll fall too far behind to succeed in ganks later.
With respect to pushing the lane, your friends are wrong in saying to never do this. It's completely situational whether to push the lane or not. If the lane is pushing against the enemy, it's often good to keep it that way because they'll have to extend to get cs and since the kill gives your laner a lead your laner can deny them cs for several waves and really build their lead (and also you can gank again). If the lane is already pushing against your ally, then definitely help clear the wave and push to turret to deny farm, get turret damage, and reset the wave. With good mechanics you can also push in a way that manipulates the wave to push against the enemy (towards your turret) after you shove to tower, which is ideal as you get tower damage and your laner can deny cs for a few waves as explained earlier.
Also, if you can take the tower after a gank, I think that's often the best decision (unless you can instead take Dragon, gank bottom then take Dragon is best case scenario).
One last note, in general don't push a Lane or tax a Lane where someone is stacking; I.e. Don't deny your nasus/veigar q stacks because it's how you normally jungle. There are exceptions to all rules.
