Split Pushing and Lane Pressure Strategies?

So, I'm a top-laner and I play champs like nasus, garen and singed who have lots of lane pressure and I was wanting to know some general rules and guidelnines for split pushing, like do you make a teleport top when your team and the other team are grouped mid or do you help your team. Also, if the enemies are missing, should you hide in the jungle until your enemies go back in lane and then push? Which is better, Zz-rot or Banner of Command? Take Both?

Thanks, looking to increase my lane pressure in games.